BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Mariya Soskova (University of Wisconsin) DTSTART:20200423T180000Z DTEND:20200423T190000Z DTSTAMP:20260404T111000Z UID:OLS/1 DESCRIPTION:Title: Fragments of the Theory of Enumeration Degrees\nby Mariya Soskova ( University of Wisconsin) as part of Online logic seminar\n\nAbstract: TBA\ n LOCATION:https://stable.researchseminars.org/talk/OLS/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Margaret Thomas (Purdue) DTSTART:20200430T180000Z DTEND:20200430T190000Z DTSTAMP:20260404T111000Z UID:OLS/2 DESCRIPTION:Title: Point counting and parameterizations\nby Margaret Thomas (Purdue) a s part of Online logic seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/OLS/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Rebecca Coulson (US Military Academy) DTSTART:20200507T180000Z DTEND:20200507T190000Z DTSTAMP:20260404T111000Z UID:OLS/3 DESCRIPTION:Title: The Bipartite Diameter 3 Metrically Homogeneous Graphs of Generic Type: Their Ages and Their Almost Sure Theories\nby Rebecca Coulson (US Mil itary Academy) as part of Online logic seminar\n\n\nAbstract\nFor the past 40 years computer scientists generally believed that\nNP-complete problem s are intractable. In particular\, Boolean\nsatisfiability (SAT)\, as a pa radigmatic automated-reasoning problem\, has\nbeen considered to be intrac table. Over the past 20 years\, however\, there\nhas been a quiet\, but dr amatic\, revolution\, and very large SAT instances\nare now being solved r outinely as part of software and hardware design.\nIn this talk I will rev iew this amazing development and show how automated\nreasoning is now an i ndustrial reality.\n\nI will then describe how we can leverage SAT solving to accomplish\nother automated-reasoning tasks. Sampling uniformly at ra ndom satisfying\ntruth assignments of a given Boolean formula or counting the number of such\nassignments are both fundamental computational problem s in computer\nscience with applications in software testing\, software sy nthesis\, machine\nlearning\, personalized learning\, and more. While the theory of these\nproblems has been thoroughly investigated since the 1980 s\, approximation\nalgorithms developed by theoreticians do not scale up t o industrial-sized\ninstances. Algorithms used by the industry offer bett er scalability\,\nbut give up certain correctness guarantees to achieve sc alability. We\ndescribe a novel approach\, based on universal hashing and Satisfiability\nModulo Theory\, that scales to formulas with hundreds of t housands of\nvariables without giving up correctness guarantees.\n LOCATION:https://stable.researchseminars.org/talk/OLS/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Chris Porter (Drake University) DTSTART:20200514T180000Z DTEND:20200514T190000Z DTSTAMP:20260404T111000Z UID:OLS/4 DESCRIPTION:Title: Randomness extraction from a computability-theoretic perspective\nb y Chris Porter (Drake University) as part of Online logic seminar\n\n\nAbs tract\nThe goal of this talk is to discuss recent work\, joint with Doug C enzer\, on a notion of the extraction rate of Turing functionals that tran slate between notions of randomness with respect to different underlying p robability measures. We will analyze several classes of extraction proced ures: a first that generalizes von Neumann's trick for extracting unbiase d randomness from the tosses of a biased coin\, a second based on work of generating biased randomness from unbiased randomness by Knuth and Yao\, a nd a third independently developed by Levin and Kautz that generalizes the data compression technique of arithmetic coding. For each of the above c lasses of extraction procedures\, we will identify a level of algorithmic randomness for an input that guarantees that we attain the corresponding e xtraction rate in producing an output. I will aim to present this materia l in a way that is accessible to logicians who are not specialists in comp utability theory / algorithmic randomness.\n LOCATION:https://stable.researchseminars.org/talk/OLS/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Moshe Vardi (Rice University) DTSTART:20200521T180000Z DTEND:20200521T190000Z DTSTAMP:20260404T111000Z UID:OLS/5 DESCRIPTION:Title: The automated-reasoning revolution: From theory to practice and back\nby Moshe Vardi (Rice University) as part of Online logic seminar\n\n\nA bstract\nFor the past 40 years computer scientists generally believed that \nNP-complete problems are intractable. In particular\, Boolean\nsatisfiab ility (SAT)\, as a paradigmatic automated-reasoning problem\, has\nbeen co nsidered to be intractable. Over the past 20 years\, however\, there\nhas been a quiet\, but dramatic\, revolution\, and very large SAT instances\na re now being solved routinely as part of software and hardware design.\nIn this talk I will review this amazing development and show how automated\n reasoning is now an industrial reality.\n\nI will then describe how we can leverage SAT solving to accomplish\nother automated-reasoning tasks. Sam pling uniformly at random satisfying\ntruth assignments of a given Boolean formula or counting the number of such\nassignments are both fundamental computational problems in computer\nscience with applications in software testing\, software synthesis\, machine\nlearning\, personalized learning\, and more. While the theory of these\nproblems has been thoroughly invest igated since the 1980s\, approximation\nalgorithms developed by theoretici ans do not scale up to industrial-sized\ninstances. Algorithms used by th e industry offer better scalability\,\nbut give up certain correctness gua rantees to achieve scalability. We\ndescribe a novel approach\, based on u niversal hashing and Satisfiability\nModulo Theory\, that scales to formul as with hundreds of thousands of\nvariables without giving up correctness guarantees.\n LOCATION:https://stable.researchseminars.org/talk/OLS/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Wesley Holliday (UC Berkeley) DTSTART:20200528T180000Z DTEND:20200528T190000Z DTSTAMP:20260404T111000Z UID:OLS/6 DESCRIPTION:Title: Extensions of choice-free Stone duality\nby Wesley Holliday (UC Ber keley) as part of Online logic seminar\n\n\nAbstract\nIn a recent paper\, “Choice-free Stone duality” (JSL\, March 2020)\, Nick Bezhanishvili an d I developed a choice-free duality theory for Boolean algebras using spec ial spectral spaces\, called upper Vietoris spaces (UV-spaces). In this ta lk\, I will cover the basics of this duality and discuss some connections to other areas of logic.\n LOCATION:https://stable.researchseminars.org/talk/OLS/6/ END:VEVENT BEGIN:VEVENT SUMMARY:William Brian (UNC Charlotte) DTSTART:20200604T180000Z DTEND:20200604T190000Z DTSTAMP:20260404T111000Z UID:OLS/7 DESCRIPTION:Title: Limited-information strategies in Banach-Mazur games\nby William Br ian (UNC Charlotte) as part of Online logic seminar\n\n\nAbstract\nThe Ban ach-Mazur game is an infinite-length game played on a topological space X\ , in which two players take turns choosing members of an infinite decreasi ng sequence of open sets\, the first player trying to ensure that the inte rsection of this sequence is empty\, and the second that it is not. A limi ted-information strategy for one of the players is a game plan that\, on a ny given move\, depends on only a small part of the game's history. In thi s talk we will discuss Telgársky's conjecture\, which asserts roughly tha t there must be topological spaces where winning strategies for the Banach Mazur game cannot be too limited\, but must rely on large parts of the ga me's history in a significant way. Recently\, it was shown that this conje cture fails in models of set theory satisfying GCH + □. In such models i t is always possible for one player to code all information concerning a g ame's history into a small piece of it. We will discuss these so-called co ding strategies\, why assuming GCH + □ makes them work so well\, and wha t can go wrong in other models of set theory.\n LOCATION:https://stable.researchseminars.org/talk/OLS/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Samaria Montenegro Guzmán (U Costa Rica) DTSTART:20200611T180000Z DTEND:20200611T190000Z DTSTAMP:20260404T111000Z UID:OLS/8 DESCRIPTION:Title: Model Theory of Pseudo Real Closed Fields\nby Samaria Montenegro Gu zmán (U Costa Rica) as part of Online logic seminar\n\n\nAbstract\nThe no tion of PAC field has been generalized by S. Basarab and by A. Prestel to ordered fields. Prestel calls a field M pseudo real closed (PRC) if M is e xistentially closed in every regular extension L to which all orderings of M extend. Thus PRC fields are to real closed fields what PAC fields are t o algebraically closed fields.\nIn this talk we will study the class of ps eudo real closed fields (PRC-fields) from a model theoretical point of vie w and we will explain some of the main results obtained. We know that the complete theory of a bounded PRC field (i.e.\, with finitely many algebrai c extensions of degree m\, for each m > 1) is NTP_2 and we have a good des cription of forking.\n\nAlso\, in a joint work with Alf Onshuus and Pierre Simon we describe the definable groups in the case that they have f-gener ics types.\n\nIn the end of the talk we will explain some results obtained with Silvain Rideau. Where we generalize the notion of PRC fields to a mo re general class of fields. In particular\, this class includes fields tha t have orders and valuations at the same time.\n LOCATION:https://stable.researchseminars.org/talk/OLS/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Rodrigo Torres-Avilés (U Bio Bio) DTSTART:20200625T180000Z DTEND:20200625T190000Z DTSTAMP:20260404T111000Z UID:OLS/9 DESCRIPTION:Title: Topological Mixing and Linear Recurrence on SMART\nby Rodrigo Torre s-Avilés (U Bio Bio) as part of Online logic seminar\n\n\nAbstract\nThe g oal of this talk is to analize recent work on properties of the subshift d erivated of a particular Turing machine\, nicknamed SMART\, which has a lo t of interesting properties (as topological minimality and aperiodicity). First\, we review a combinatorial proof of the Topological Mixing property of the subshift derivated from SMART\, and later\, we deepen to tie gener al subshift of Turing Machines with more general properties\, as linear re currence.\n LOCATION:https://stable.researchseminars.org/talk/OLS/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Henry Towsner (U Penn) DTSTART:20200709T180000Z DTEND:20200709T190000Z DTSTAMP:20260404T111000Z UID:OLS/11 DESCRIPTION:Title: Should we believe in nonstandard analysis?\nby Henry Towsner (U Pe nn) as part of Online logic seminar\n\n\nAbstract\nNonstandard analysis ha s been the one of the focal points for debate about the role of the axiom of choice in mathematics. I'll argue that this discussion often conflates two distinct issues - the question of whether mathematical arguments are valid\, and the question of whether all mathematical objects should be und erstood to "exist" in the same way. I'll discuss various ways of showing that most uses of nonstandard analysis in mathematics don't actually use t he axiom of choice\, and how this perspective can be used to obtain new ma thematical results (including applications\, joint with William Simmons\, to finding new bounds for primality testing in polynomial rings). On the other hand\, I'll argue (based on joint work with Kenny Easwaran) that the same perspective argues against interpreting nonstandard values too liter ally when considering applications with real-world interpretations.\n LOCATION:https://stable.researchseminars.org/talk/OLS/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Elaine Pimentel (DMAT/UFRN) DTSTART:20200618T180000Z DTEND:20200618T190000Z DTSTAMP:20260404T111000Z UID:OLS/12 DESCRIPTION:Title: A game model for proofs with costs\nby Elaine Pimentel (DMAT/UFRN) as part of Online logic seminar\n\n\nAbstract\nWe look at substructural c alculi from a game semantic point of view\, guided by certain intuitions a bout resource conscious and\, more specifically\, cost conscious reasoning . To this aim\, we start with a game\, where player I defends a claim corr esponding to a (single-conclusion) sequent\, while player II tries to refu te that claim. Branching rules for additive connectives are modeled by cho ices of II\, while branching for multiplicative connectives leads to split ting the game into parallel subgames\, all of which have to be won by play er I to succeed. The game comes into full swing by adding cost labels to a ssumptions\, and a corresponding budget. Different proofs of the same end- sequent are interpreted as more or less expensive strategies for \\I to de fend the corresponding claim. This leads to a new kind of labelled calculu s\, which can be seen as a fragment of SELL (subexponential linear logic). Finally\, we generalize the concept of costs in proofs by using a semiri ng structure\, illustrate our interpretation by examples and investigate s ome proof-theoretical properties.\nThis is a joint work with Timo Lang\, C arlos Olarte and Christian G. Fermüller\n LOCATION:https://stable.researchseminars.org/talk/OLS/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Linda Brown Westrick (Penn State) DTSTART:20200716T180000Z DTEND:20200716T190000Z DTSTAMP:20260404T111000Z UID:OLS/13 DESCRIPTION:Title: Borel combinatorics fail in HYP\nby Linda Brown Westrick (Penn Sta te) as part of Online logic seminar\n\n\nAbstract\nWe show that the Borel Dual Ramsey Theorem fails in HYP\, regardless of the number of partitions k ≥ 2. Therefore\, the Borel Dual Ramsey Theorem is not a statement of h yperarithmetic analysis. We also apply similar methods\, namely constructi on of completely determined pseudo-Borel codes via decorating trees\, to o btain results concerning some theorems about Borel graph coloring and the prisoner hat problem. Joint work with Henry Towsner and Rose Weisshaar.\n LOCATION:https://stable.researchseminars.org/talk/OLS/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Dana Bartošová (U Florida) DTSTART:20200723T180000Z DTEND:20200723T190000Z DTSTAMP:20260404T111000Z UID:OLS/14 DESCRIPTION:Title: Dynamics of finite products of groups and of group extensions\nby Dana Bartošová (U Florida) as part of Online logic seminar\n\n\nAbstract \nWe will investigate how universal minimal flows interact with group oper ations. We show that the universal minimal flow of the product of two copi es of integers is far from the product of two copies of the universal mini mal flow of integers. On the other hand\, when a topological group is a gr oup extension of a compact group by a discrete group\, then the universal minimal flow can be computed from the discrete and compact parts.\n LOCATION:https://stable.researchseminars.org/talk/OLS/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Ruiyuan Chen (U Illinois Urbana-Champaign) DTSTART:20200702T180000Z DTEND:20200702T190000Z DTSTAMP:20260404T111000Z UID:OLS/15 DESCRIPTION:Title: Stone duality and strong conceptual completeness for infinitary logic< /a>\nby Ruiyuan Chen (U Illinois Urbana-Champaign) as part of Online logic seminar\n\n\nAbstract\nThe classical Stone duality\, applied to the Linde nbaum-Tarski\nalgebra of a propositional theory\, allows the syntax of the theory to be\ncanonically recovered from its space of models\; this encom passes both\nthe completeness and definability theorems for propositional logic.\nMany known variants and generalizations of Stone duality have anal ogous\ninterpretations as completeness-definability theorems for various\n fragments of finitary propositional and first-order logic. In this\ntalk\ , I will give an overview of this duality-theoretic approach to\ncompleten ess\, including the key examples of Stone duality as well as\nMakkai duali ty for first-order logic. I will then present a duality\ntheorem for the countably infinitary first-order logic\n$L_{\\omega_1\\omega}$\, proved us ing tools from invariant descriptive set\ntheory as well as topos theory.\ n LOCATION:https://stable.researchseminars.org/talk/OLS/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Manuela Busaniche (CCT CONICET Santa Fe) DTSTART:20200730T180000Z DTEND:20200730T190000Z DTSTAMP:20260404T111000Z UID:OLS/16 DESCRIPTION:Title: Residuated Lattices: algebraic constructions related to substructural logics\nby Manuela Busaniche (CCT CONICET Santa Fe) as part of Online logic seminar\n\n\nAbstract\nSubstructural logics are logics that\, when t hey are formulated in a Gentzen style system\, they lack some of the struc tural rules: contraction\, weakening or exchange.The importance of the the ory of substructural logics relies on the fact that they provide a common framework where different logical systems can be compared. They include in tuitionistic logic\, fuzzy logics\, relevance logics\, linear logic\, many -valued logics and others.\n\nTheir algebraic semantics are based on resid uated lattices. The class of these ordered algebraic structures is quite b ig and hard to study\, but it contains some proper subclasses that are wel l-known such as Boolean algebras\, Heyting algebras\, MV-algebras. In this talk we will see different constructions of new residuated lattices based on better-known algebras.\n LOCATION:https://stable.researchseminars.org/talk/OLS/16/ END:VEVENT BEGIN:VEVENT SUMMARY:James Worrell (U of Oxford) DTSTART:20200806T180000Z DTEND:20200806T190000Z DTSTAMP:20260404T111000Z UID:OLS/17 DESCRIPTION:Title: Decision problems in program analysis\nby James Worrell (U of Oxfo rd) as part of Online logic seminar\n\n\nAbstract\nWe consider decision pr oblems for affine programs: a simple model from the field of program analy sis. In this talk we focus on deciding the existence of algebraic and semi -algebraic invariants that separate reachable from non-reachable program s tates\, and on deciding termination. We will survey some recently obtained decision procedures for these problems\, and highlight some longstanding open questions.\n LOCATION:https://stable.researchseminars.org/talk/OLS/17/ END:VEVENT BEGIN:VEVENT SUMMARY:James Hanson (U of Wisconsin) DTSTART:20200813T180000Z DTEND:20200813T190000Z DTSTAMP:20260404T111000Z UID:OLS/18 DESCRIPTION:Title: Strongly Minimal Sets in Continuous Logic\nby James Hanson (U of W isconsin) as part of Online logic seminar\n\n\nAbstract\nContinuous logic is a generalization of first-order logic suited to studying structures wit h a real-valued metric. There is a natural generalization of the notion of strongly minimal sets to continuous logic\, and\, while they do not play quite the same role in characterizing theories categorical in uncountable cardinalities\, they are interesting in their own right. After developing some of the basic machinery of strongly minimal sets in continuous logic\, we will characterize the essentially continuous strongly minimal theories \, i.e. those which do not interpret an infinite discrete structure\, and we will leverage this into a precise characterization of the essentially c ontinuous strongly minimal groups.\n LOCATION:https://stable.researchseminars.org/talk/OLS/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Damir Dzhafarov (U of Connecticut) DTSTART:20200820T180000Z DTEND:20200820T190000Z DTSTAMP:20260404T111000Z UID:OLS/19 DESCRIPTION:Title: Milliken's tree theorem and computability theory\nby Damir Dzhafar ov (U of Connecticut) as part of Online logic seminar\n\n\nAbstract\nMilli ken's tree theorem is a powerful combinatorial result that generalized Ram sey's theorem and many other familiar partition results. I will present re cent work on the effective and proof-theoretic strength of this theorem\, which was originally motivated by a question of Dobrinen. The main result is a complete characterization of Milliken's tree theorem in terms of reve rse mathematics and the usual computability-theoretic hierarchies\, along with several applications to other combinatorial problems. Key to this is a new inductive proof of Milliken's tree theorem\, employing an effective version of the Halpern-Lauchli theorem. This is joint work with Angles d'A uriac\, Cholak\, Monin\, and Patey.\n LOCATION:https://stable.researchseminars.org/talk/OLS/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Mirna Džamonja (IHPST\, CNRS-Université Panthéon-Sorbonne Paris \, France) DTSTART:20200910T180000Z DTEND:20200910T190000Z DTSTAMP:20260404T111000Z UID:OLS/20 DESCRIPTION:Title: On logics that make a bridge from the Discrete to the Continuous\n by Mirna Džamonja (IHPST\, CNRS-Université Panthéon-Sorbonne Paris\, Fr ance) as part of Online logic seminar\n\n\nAbstract\nWe study logics which model the passage between an infinite sequence of finite models to an unc ountable limiting object\, such as is the case in the context of graphons. Of particular interest is the connection between the countable and the un countable object that one obtains as the union versus the combinatorial li mit of the same sequence.\n LOCATION:https://stable.researchseminars.org/talk/OLS/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Carl Mummert (Marshall University) DTSTART:20200903T180000Z DTEND:20200903T190000Z DTSTAMP:20260404T111000Z UID:OLS/21 DESCRIPTION:Title: The strength of König's edge coloring theorem\nby Carl Mummert (M arshall University) as part of Online logic seminar\n\n\nAbstract\nKönig' s edge coloring theorem says that a bipartite graph with\nmaximal degree $ n$ has an edge coloring with no more than $n$ colors.\nWe study the comput ability theory and Reverse Mathematics of this theorem. Computable biparti te graphs with degree bounded by $n$ have computable edge colorings with $ 2n-1$ colors\, but the theorem that there is an edge coloring with $n$ col ors is equivalent to $\\mathsf{WKL}_0$ over $\\mathsf{RCA}_0$. The number of colors permitted affects the computability of the solution. We obtain an additional proof of the following theorem of Paul Shafer: $\\mathsf{W KL}_0$ is equivalent over $\\mathsf{RCA}_0$ to the \nprinciple that a coun table bipartite n-regular graph is the union of n complete matchings.\n LOCATION:https://stable.researchseminars.org/talk/OLS/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Dima Sinapova (U Illinois Chicago) DTSTART:20200827T180000Z DTEND:20200827T190000Z DTSTAMP:20260404T111000Z UID:OLS/22 DESCRIPTION:Title: Iteration\, reflection\, and Prikry forcing\nby Dima Sinapova (U I llinois Chicago) as part of Online logic seminar\n\n\nAbstract\nThere is a n inherent tension between stationary reflection and the failure of the si ngular cardinal hypothesis (SCH). The former is a compactness type princip le that follows from large cardinals. Compactness is the phenomenon where if a certain property holds for every smaller substructure of an object\, then it holds for the entire object. In contrast\, failure of SCH is an in stance of incompactness. It is usually obtained using Prikry forcing.\n\nW e describe a Prikry style iteration\, and use it to force stationary refle ction in the presence of not SCH. Then we discuss the situation at smaller cardinals. This is joint work with Alejandro Poveda and Assaf Rinot.\n LOCATION:https://stable.researchseminars.org/talk/OLS/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Berenstein (U de los Andes) DTSTART:20200917T180000Z DTEND:20200917T190000Z DTSTAMP:20260404T111000Z UID:OLS/23 DESCRIPTION:Title: Expansions of geometric theories as measurable structures\nby Alex ander Berenstein (U de los Andes) as part of Online logic seminar\n\n\nAbs tract\nWe say that a theory T is geometric if for any model $M\\models T$ the algebraic closure satisfies the exchange property and T eliminates the quantifier $\\exists^{\\infty}$. We will explain how to define\, inside a geometric theory\, a well behaved notion of dimension for definable sets. We will then consider the special case where the underlying theory is mea surable (in the sense of Macpherson and Steinhorn) of SU-rk one\, where be sides a dimension we can also assign a measure to definable sets. We will then introduce an expansion called an H-structures and show that it can be studied as a generalized measurable structure whose dimension has values in $\\omega^2$. This is joint work with García and Zou.\n LOCATION:https://stable.researchseminars.org/talk/OLS/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Victoria Noquez (Indiana University) DTSTART:20201001T180000Z DTEND:20201001T190000Z DTSTAMP:20260404T111000Z UID:OLS/24 DESCRIPTION:Title: The Sierpinski Carpet as a Final Coalgebra Obtained by Completing an I nitial Algebra\nby Victoria Noquez (Indiana University) as part of Onl ine logic seminar\n\n\nAbstract\nThe background for this work includes Fre yd's Theorem\, in which the unit interval is viewed as a final coalgebra o f a certain endofunctor in the category of bipointed sets. Leinster genera lized this to a broad class of self-similar spaces in categories of sets\, also characterizing them as topological spaces. Bhattacharya\, Moss\, Rat nayake\, and Rose went in a different direction\, working in categories of metric spaces\, obtaining the unit interval and the Sierpinski Gasket as a final colagebras in the categories of bipointed and tripointed metric sp aces respectively. To achieve this they used a Cauchy completion of an ini tial algebra to obtain the required final coalgebra. In their examples\, t he iterations of the fractals can be viewed as gluing together a finite nu mber of scaled copies of some set at some finite set of points (e.g. corne rs of triangles). Here we will expand these ideas to apply to a broader cl ass of fractals\, in which copies of some set are glued along segments (e. g. sides of a square). We use the method of completing an initial algebra to obtain the Sierpinski Carpet as a final coalgebra in a category of metr ic spaces\, and note the required adaptations to this approach\, most nota bly that we no longer get the initial algebra as the colimit of a countabl e sequence of metric spaces. We will explore some ways in which these resu lts may be further generalized to a broader class of fractals. Joint work with Larry Moss.\n LOCATION:https://stable.researchseminars.org/talk/OLS/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Anush Tserunyan (McGill University) DTSTART:20201119T190000Z DTEND:20201119T200000Z DTSTAMP:20260404T111000Z UID:OLS/25 DESCRIPTION:Title: Containers made easy\nby Anush Tserunyan (McGill University) as pa rt of Online logic seminar\n\n\nAbstract\nA modern trend in extremal combi natorics is extending classical results from the dense setting (e.g. Szeme ré\;di's theorem) to the sparse random setting. More precisely\, one shows that a property of a given ``dense'' structure is inherited by a ra ndomly chosen ``sparse'' substructure. A recent breakthrough tool for prov ing such statements is the Balogh--Morris--Samotij and Saxton--Thomason hy pergraph containers method\, which bounds the number of independent sets i n homogeneously dense finite hypergraphs\, thus implying that a random spa rse subset is not independent. In a joint work with A. Bernshteyn\, M. Del court\, and H. Towsner\, we give a new --- elementary and nonalgorithmic - -- proof of the containers theorem for finite hypergraphs. Our proof is in spired by considering hyperfinite hypergraphs in the setting of nonstandar d analysis\, where there is a notion of dimension capturing the logarithmi c rate of growth of finite sets. Applying this intuition in another settin g with a notion of dimension\, namely\, algebraically closed fields\, A. B ernshteyn\, M. Delcourt\, and I prove an analogous theorem for ``dense'' a lgebraically definable hypergraphs: any Zariski-generic low-dimensional su bset of such hypergraphs is itself ``dense'' (in particular\, not independ ent).\n LOCATION:https://stable.researchseminars.org/talk/OLS/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Arno Pauly (Swansea University) DTSTART:20200924T180000Z DTEND:20200924T190000Z DTSTAMP:20260404T111000Z UID:OLS/27 DESCRIPTION:Title: How computability-theoretic degree structures and topological spaces a re related\nby Arno Pauly (Swansea University) as part of Online logic seminar\n\n\nAbstract\nWe can generalize Turing reducibility to points in a large class of topological spaces. The point degree spectrum of a space is the collection of the degrees of its points. This is always a collecti on of Medvedev degrees\, and it turns out that topological properties of t he space are closely related to what degrees occur in it. For example\, a Polish space has only Turing degrees iff it is countably dimensional. This connection can be used to bring topological techniques to bear on problem s from computability theory and vice versa. The talk is based on joint wor k with Takayuki Kihara and Keng Meng Ng (https://arxiv.org/abs/1405.6866 a nd https://arxiv.org/abs/1904.04107).\n LOCATION:https://stable.researchseminars.org/talk/OLS/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Johanna Franklin (Hofstra University) DTSTART:20201203T190000Z DTEND:20201203T200000Z DTSTAMP:20260404T111000Z UID:OLS/28 DESCRIPTION:Title: Limiting densities and finitely presented structures\nby Johanna F ranklin (Hofstra University) as part of Online logic seminar\n\n\nAbstract \nWe address the question of typicality for structures by studying the lim iting densities of various properties. We define the limiting density of a property Q to be the limit of the fraction of presentations of a variety with relators of length at most s that have property Q as s goes to infini ty. After providing some initial examples\, we present a more general appr oach to our question. This work is joint with Meng-Che "Turbo" Ho and Juli a Knight.\n LOCATION:https://stable.researchseminars.org/talk/OLS/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Angeliki Koutsoukou-Argyraki (U of Cambridge) DTSTART:20210121T190000Z DTEND:20210121T200000Z DTSTAMP:20260404T111000Z UID:OLS/29 DESCRIPTION:Title: Aristotle's Assertoric Syllogistic in Isabelle/HOL\nby Angeliki Ko utsoukou-Argyraki (U of Cambridge) as part of Online logic seminar\n\n\nAb stract\nI discuss my formalisation of some basic elements of\nAristotle's assertoric syllogistic\nusing the proof assistant (interactive theorem pro ver) Isabelle/HOL. The\nformal proof development can\nbe found on the Archive of Formal Proofs\n LOCATION:https://stable.researchseminars.org/talk/OLS/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Aleksandra Kwiatkowska (U of Wrocław) DTSTART:20210114T190000Z DTEND:20210114T200000Z DTSTAMP:20260404T111000Z UID:OLS/30 DESCRIPTION:Title: Simplicity of the automorphism groups of countable homogeneous structu res\nby Aleksandra Kwiatkowska (U of Wrocław) as part of Online logic seminar\n\n\nAbstract\nThe program of understanding the normal subgroup s tructure of groups that arise as automorphism groups of countable structur es dates back at least to the ’50s\, when Higman described all proper no rmal subgroups of the automorphism group of rationals (Q\,<). In recent se veral years Tent-Ziegler\, following the work of Macpherson-Tent\, proved simplicity for many automorphism groups of countable graphs and metric spa ces. In the talk\, we prove simplicity for the automorphism groups of orde r and tournament expansions of homogeneous structures such as the bounded Urysohn metric space and the random graph. In particular\, we show that th e automorphism group of the linearly ordered random graph is a simple grou p. This is joint work with Filippo Calderoni and Katrin Tent.\n LOCATION:https://stable.researchseminars.org/talk/OLS/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Steffen Lempp (U of Wisconsin) DTSTART:20201022T180000Z DTEND:20201022T190000Z DTSTAMP:20260404T111000Z UID:OLS/31 DESCRIPTION:Title: The Turing Degrees: On the Order Dimension of and Embeddings into the Turing Degrees\nby Steffen Lempp (U of Wisconsin) as part of Online lo gic seminar\n\n\nAbstract\nIn joint work with Higuchi\, Raghavan and Steph an\, we show that the order dimension of any locally countable partial ord ering (P\, <) of size κ+\, for any κ of uncountable cofinality\, is at m ost κ.\nIn particular\, this implies that it is consistent with ZFC that the dimension of the Turing degrees under partial ordering can be strictly less than the continuum. (Kumar and Raghavan have since shown that it can also be continuum\, thus the order dimension of the Turing degrees is ind ependent of ZFC.)\nThis is closely related to an old question of Sacks fro m 1963 about whether the Turing degrees form a universal locally countable partial order of size continuum.\n LOCATION:https://stable.researchseminars.org/talk/OLS/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Lynn Scow (Cal State San Bernardino) DTSTART:20201112T190000Z DTEND:20201112T200000Z DTSTAMP:20260404T111000Z UID:OLS/32 DESCRIPTION:Title: Transfer of the Ramsey property\nby Lynn Scow (Cal State San Berna rdino) as part of Online logic seminar\n\n\nAbstract\nRamsey's theorem for finite sequences is a special case of a class of finite structures having the Ramsey property\, where that class is the age of $(\\mathbb{Q}\,<)$. Given two classes $\\mathcal{K}_1$\nand $\\mathcal{K}_2$\, each with the Ramsey property\, there are many lenses through which one might examine ho w the Ramsey property transfers from $\\mathcal{K}_1$ to $\\mathcal{K}_2$. We will present some approaches.\n LOCATION:https://stable.researchseminars.org/talk/OLS/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Adam Přenosil (Vanderbilt University) DTSTART:20201029T180000Z DTEND:20201029T190000Z DTSTAMP:20260404T111000Z UID:OLS/33 DESCRIPTION:Title: Semisimplicity\, Glivenko theorems\, and the excluded middle\nby A dam Přenosil (Vanderbilt University) as part of Online logic seminar\n\n\ nAbstract\nThere are at least three different ways to obtain classical pro positional logic from intuitionistic propositional logic. Firstly\, it is the extension of intuitionistic logic by the law of the excluded middle (L EM). Secondly\, it is related to intuitionistic logic by the double-negati on translation of Glivenko. Finally\, the algebraic models of classical lo gic are precisely the semisimple algebraic models of intuitionistic logic (i.e. Boolean algebras are precisely the semisimple Heyting algebras). We show how to formulate the equivalence between the LEM and semisimplicity\, and between what we might call the Glivenko companion and the semisimple companion of a logic\, at an appropriate level of generality. This equival ence will subsume several existing Glivenko-like theorems\, as well as som e new ones. It also provides a useful technique for describing the semisim ple subvarieties of a given variety of algebras. This is joint work with T omáš Lávička\, building on previous work by James Raftery.\n LOCATION:https://stable.researchseminars.org/talk/OLS/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter Cholak (University of Notre Dame) DTSTART:20210204T190000Z DTEND:20210204T200000Z DTSTAMP:20260404T111000Z UID:OLS/35 DESCRIPTION:Title: Old and new results on the computably enumerable sets\nby Peter Ch olak (University of Notre Dame) as part of Online logic seminar\n\n\nAbstr act\nWe will survey a number of old results on the computably enumerable s ets and finish with a few new results. The computably enumerable sets are interesting since anything which can happen computably happens in computa bly enumerable sets.\n LOCATION:https://stable.researchseminars.org/talk/OLS/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Farzaneh Derakhshan (Carnegie Mellon) DTSTART:20201105T190000Z DTEND:20201105T200000Z DTSTAMP:20260404T111000Z UID:OLS/36 DESCRIPTION:Title: Strong Progress for Session-Typed Processes in a Linear Metalogic with Circular Proofs\nby Farzaneh Derakhshan (Carnegie Mellon) as part of Online logic seminar\n\n\nAbstract\nSession types describe the communicati on behavior of interacting processes. Binary session types are a particula r form of session types in which each channel has two endpoints. The stron g progress property states that a recursive process either terminates or c ommunicates along one of its external channels after a finite number of st eps. In this talk\, I show how to prove strong progress for valid session- typed processes defined in an asynchronous computational semantics\, worki ng in a fragment of binary session types in which a process can use at mos t one resource. We formalize a proof of strong progress via a processes-as -formulas interpretation into a metalogic that we have introduced. The met alogic is an infinitary first order linear calculus with least and greates t fixed-points. We build a circular derivation for the strong progress pro perty of processes in this first order calculus. By enforcing a condition on the logical derivations\, we ensure their cut elimination property and soundness of the strong progress theorem.\n LOCATION:https://stable.researchseminars.org/talk/OLS/36/ END:VEVENT BEGIN:VEVENT SUMMARY:John Baldwin (University of Illinois\, Chicago) DTSTART:20201015T180000Z DTEND:20201015T190000Z DTSTAMP:20260404T111000Z UID:OLS/37 DESCRIPTION:Title: Towards a finer classification of Strongly minimal sets\nby John B aldwin (University of Illinois\, Chicago) as part of Online logic seminar\ n\n\nAbstract\nPDF Abstract posted on Seminar Web page at http://la grange.math.siu.edu/calvert/OnlineSeminar/Baldwin201015ab.pdf\n LOCATION:https://stable.researchseminars.org/talk/OLS/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Artem Chernikov (UCLA) DTSTART:20201008T180000Z DTEND:20201008T190000Z DTSTAMP:20260404T111000Z UID:OLS/38 DESCRIPTION:Title: Idempotent Keisler measures\nby Artem Chernikov (UCLA) as part of Online logic seminar\n\n\nAbstract\nIn model theory\, a type is an ultrafi lter on the Boolean algebra of definable sets\, and is the same thing as a finitely additive {0\,1}-valued measure. This is a special kind of a Keis ler measure\, which is just a finitely additive real-valued probability me asure on the Boolean algebra of definable sets. If the structure we are co nsidering expands a group (i.e. the group operations are definable)\, it o ften lifts to a natural semigroup operation on the space of its types/meas ures\, and it makes sense to talk about the idempotent ones among them. Fo r instance\, idempotent ultrafilters on the integers provide an elegant pr oof of Hindman's theorem\, and fit into this setting taking the structure to be (Z\,+) with all of its subsets named by predicates. On the other han d\, in the context of locally compact abelian groups\, classical work by W endel\, Rudin\, Cohen (before inventing forcing) and others classifies ide mpotent Borel measures\, showing that they are precisely the Haar measures of compact subgroups. I will discuss recent joint work with Kyle Gannon a iming to unify these two settings\, leading in particular to a classificat ion of idempotent Keisler measures in stable theories.\n LOCATION:https://stable.researchseminars.org/talk/OLS/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Gil Sagi (U of Haifa) DTSTART:20201210T190000Z DTEND:20201210T200000Z DTSTAMP:20260404T111000Z UID:OLS/39 DESCRIPTION:Title: Formalization\, Commitments and Constraints\nby Gil Sagi (U of Hai fa) as part of Online logic seminar\n\n\nAbstract\nThe topic of this talk is formalization: the assignment of formal language arguments to natural l anguage arguments for the sake of evaluating the latter's validity. It has been recognized in the literature that formalization is far from a trivia l process. One must discern the logical from the nonlogical in the sentenc e\, a process that requires theorizing that goes beyond the mere understan ding of the sentence formalized (Brun 2014). Moreover\, according to some\ , formalization is a form of explication\, and it "involves creative and n ormative aspects of constructing logical forms" (ibid).\n\nIn previous wor k\, I proposed a model-theoretic framework of "semantic constraints\," whe re there is no strict distinction between logical and nonlogical vocabular y. The form of sentences in a formal language is determined rather by a se t of constraints on models. In the talk\, I will show how this framework c an also be used in the process of formalization\, where the semantic const raints are conceived of as commitments made with respect to the language. I will extend the framework to include "formalization constraints" on func tions taking arguments from a source language to a target language\, and I will consider various meta-constraints on both the process of formalizati on and its end result.\n LOCATION:https://stable.researchseminars.org/talk/OLS/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Raimundo Briceño (Pontificia Universidad Católica de Chile) DTSTART:20210128T190000Z DTEND:20210128T200000Z DTSTAMP:20260404T111000Z UID:OLS/40 DESCRIPTION:Title: Dismantlability\, connectedness\, and mixing in relational structures< /a>\nby Raimundo Briceño (Pontificia Universidad Católica de Chile) as p art of Online logic seminar\n\n\nAbstract\nThe Constraint Satisfaction Pro blem (CSP) and its counting counterpart appears under different guises in many areas of mathematics\, computer science\, and elsewhere. Its structur al and algorithmic properties have demonstrated to play a crucial role in many of those applications. For instance\, in the decision CSPs\, structur al properties of the relational structures involved —like\, for example\ , dismantlability— and their logical characterizations have been instrum ental for determining the complexity and other properties of the problem. Topological properties of the solution set such as connectedness are relat ed to the hardness of CSPs over random structures. Additionally\, in appro ximate counting and statistical physics\, where CSPs emerge in the form of spin systems\, mixing properties and the uniqueness of Gibbs measures hav e been heavily exploited for approximating partition functions and free en ergy.\n\nIn spite of the great diversity of those features\, there are som e eerie similarities between them. These were observed and made more preci se in the case of graph homomorphisms by Brightwell and Winkler\, who show ed that dismantlability of the target graph\, connectedness of the set of homomorphisms\, and good mixing properties of the corresponding spin syste m are all equivalent. In this talk we go a step further and demonstrate si milar connections for arbitrary CSPs. This requires a much deeper understa nding of dismantling and the structure of the solution space in the case o f relational structures\, and also new refined concepts of mixing. In addi tion\, we develop properties related to the study of valid extensions of a given partially defined homomorphism\, an approach that turns out to be n ovel even in the graph case. We also add to the mix the combinatorial prop erty of finite duality and its logic counterpart\, FO-definability\, studi ed by Larose\, Loten\, and Tardif. This is joint work with Andrei Bulatov\ , Víctor Dalmau\, and Benoît Larose.\n LOCATION:https://stable.researchseminars.org/talk/OLS/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Marcos Mazari-Armida (Carnegie Mellon University) DTSTART:20210218T190000Z DTEND:20210218T200000Z DTSTAMP:20260404T111000Z UID:OLS/41 DESCRIPTION:Title: Characterizing noetherian rings via superstability\nby Marcos Maza ri-Armida (Carnegie Mellon University) as part of Online logic seminar\n\n \nAbstract\nWe will show how superstability of certain classes of modules can be used to characterize noetherian rings. None of the classes of modul es that we will consider are axiomatizable by a complete first-order theor y and some of them are not even first-order axiomatizable\, but they are a ll Abstract Elementary Classes (AECs). This new way of looking at classes of modules as AECs will be emphasized as I think it can have interesting a pplications. If time permits we will see how the ideas presented can be us ed to characterize other classical rings such as pure-semisimple rings and perfect rings.\n LOCATION:https://stable.researchseminars.org/talk/OLS/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Sarah Reitzes (U of Chicago) DTSTART:20210415T180000Z DTEND:20210415T190000Z DTSTAMP:20260404T111000Z UID:OLS/42 DESCRIPTION:Title: Reduction games over $\\textup{RCA}_0$\nby Sarah Reitzes (U of Chi cago) as part of Online logic seminar\n\n\nAbstract\nIn this talk\, I will discuss joint work with Damir D. Dzhafarov and Denis R. Hirschfeldt. Our work centers on the characterization of problems P and Q such that P $\\le q_{\\omega}$ Q\, as well as problems P and Q such that\n$\\textup{RCA}_0 \ \vdash$ Q $\\to$ P\, in terms of winning strategies in certain games. Thes e characterizations were originally introduced by Hirschfeldt and Jockusch . I will discuss extensions and generalizations of these characterizations \, including a certain\nnotion of compactness that allows us\, for strateg ies satisfying particular conditions\, to bound the number of moves it tak es to win. This bound is independent of the instance of the problem P bein g considered. This allows us to develop the idea of Weihrauch\nand general ized Weihrauch reduction over some base theory. Here\, we will focus on th e base theory $\\textup{RCA}_0$. In this talk\, I will explore these notio ns of reduction among various principles\, focusing particularly on boundi ng and induction principles.\n LOCATION:https://stable.researchseminars.org/talk/OLS/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Ludovic Patey (Institut Camille Jordan\, Lyon) DTSTART:20210211T190000Z DTEND:20210211T200000Z DTSTAMP:20260404T111000Z UID:OLS/43 DESCRIPTION:Title: Canonical notions of forcing in computability theory\nby Ludovic P atey (Institut Camille Jordan\, Lyon) as part of Online logic seminar\n\n\ nAbstract\nIn reverse mathematics\, a proof that a problem P does not impl y a problem Q is usually done by constructing a computable instance of Q w hose solutions are computationally complex\, while proving that every simp le instance of P has a simple solution\, using a notion of forcing. In its full generality\, the notion of forcing could depend on both P and Q\, bu t in most cases\, the notion of forcing for building solutions to P does n ot depend on Q. This suggests the existence of a "canonical" notion of for cing for P\, that is\, a notion of forcing such that all the relevant sepa ration proofs can be obtained without loss of generality with sufficiently generic sets for this notion. We settle a formal framework for discussing this question\, and give preliminary results. This is a joint work with D enis Hirschfeldt.\n LOCATION:https://stable.researchseminars.org/talk/OLS/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Dakota Ihli (U of Illinois Urbana-Champaign) DTSTART:20210304T190000Z DTEND:20210304T200000Z DTSTAMP:20260404T111000Z UID:OLS/44 DESCRIPTION:Title: What generic automorphisms of the random poset look like\nby Dakot a Ihli (U of Illinois Urbana-Champaign) as part of Online logic seminar\n\ n\nAbstract\nThe random poset (the Fraïssé limit of the class of finite\ nposets) admits generic automorphisms — that is\, its automorphism group \nadmits a comeagre conjugacy class. This result\, due to D. Kuske and J.\ nTruss\, was proven without explicitly describing the automorphisms in\nqu estion. Here we give a new\, concrete description of the generic\nautomorp hisms\, and we discuss the combinatorics and model theory involved.\n LOCATION:https://stable.researchseminars.org/talk/OLS/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Sophia Knight (University of Minnesota\, Duluth) DTSTART:20210225T190000Z DTEND:20210225T200000Z DTSTAMP:20260404T111000Z UID:OLS/45 DESCRIPTION:Title: Reasoning about agents who may know other agents’ strategies in Stra tegy Logic\nby Sophia Knight (University of Minnesota\, Duluth) as par t of Online logic seminar\n\n\nAbstract\nIn this talk I will discuss some new developments in Strategy Logic with imperfect information. Strategy Lo gic is concerned with agents' strategic abilities in multi-agent systems\, and unlike ATL\, treats strategies as first-class objects in the logic\, independent from the agents. Thus\, in imperfect information settings\, St rategy Logic raises delicate issues\, such as what agents know about one a nother's strategies. I will describe a new version of Strategy Logic that ensures that agents' strategies are uniform\, and allows a formal descript ion of their knowledge about each other's strategies.\n LOCATION:https://stable.researchseminars.org/talk/OLS/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Lieberman (Brno University of Technology) DTSTART:20210325T180000Z DTEND:20210325T190000Z DTSTAMP:20260404T111000Z UID:OLS/46 DESCRIPTION:Title: Recent developments in categorical model theory\nby Michael Lieber man (Brno University of Technology) as part of Online logic seminar\n\n\nA bstract\nWe give an overview of the foundations of the still-emerging fiel d of categorical model theory\, which synthesizes ideas and methods drawn from accessible categories\, abstract model theory\, and set theory. We d iscuss the fundamental nexus of interaction---a very slight generalization of abstract elementary classes (AECs)---and sketch a few recent results. In particular\, we consider:\n-Connections between compact cardinals\, ta meness of Galois types\, and the closure of images of accessible functors (joint work with Will Boney).\n-Stable independence on an abstract categor y\, with surprising connections to homotopy theory (joint work with Jiří Rosický and Sebastien Vasey).\n LOCATION:https://stable.researchseminars.org/talk/OLS/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Matthew Moore (U of Kansas) DTSTART:20210311T190000Z DTEND:20210311T200000Z DTSTAMP:20260404T111000Z UID:OLS/47 DESCRIPTION:Title: The Hidden Subgroup Problem for Universal Algebras\nby Matthew Moo re (U of Kansas) as part of Online logic seminar\n\n\nAbstract\nThe Hidden Subgroup Problem (HSP) is a computational problem which includes as\nspec ial cases integer factorization\, the discrete logarithm problem\, graph\n isomorphism\, and the shortest vector problem. The celebrated polynomial-t ime\nquantum algorithms for factorization and the discrete logarithm are r estricted\nversions of a generic polynomial-time quantum solution to the H SP for\nabelian groups\, but despite focused research no polynomial -time solution\nfor general groups has yet been found. We propose a genera lization of the HSP to\ninclude arbitrary algebraic structures and analyze this new problem on\npowers of 2-element algebras. We prove a comp lete classification of every such\npower as quantum tractable (i.e. polyno mial-time)\, classically tractable\,\nquantum intractable\, or classically intractable. In particular\, we identify a\nclass of algebras for which t he generalized HSP exhibits super-polynomial\nspeedup on a quantum compute r compared to a classical one.\n LOCATION:https://stable.researchseminars.org/talk/OLS/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Deirdre Haskell (McMaster University) DTSTART:20210401T180000Z DTEND:20210401T190000Z DTSTAMP:20260404T111000Z UID:OLS/48 DESCRIPTION:Title: Tameness properties of theories of valued fields with analytic functio ns\nby Deirdre Haskell (McMaster University) as part of Online logic s eminar\n\n\nAbstract\nAn important motif in model-theoretic algebra over t he last thirty years has been the concept of tameness and the impact it ha s for understanding the definable sets of a structure. In this talk\, I wi ll describe some of the ways this motif occurs in the case of valued field s\, especially ordered convexly valued fields\, when equipped with additio nal function symbols which\, on the standard model\, are interpreted by fu nctions defined by convergent power series. All of these notions will be d efined in the course of the talk.\n LOCATION:https://stable.researchseminars.org/talk/OLS/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Mariana Vicaria (Berkeley) DTSTART:20210429T180000Z DTEND:20210429T190000Z DTSTAMP:20260404T111000Z UID:OLS/49 DESCRIPTION:Title: Elimination of imaginaries and stable domination in multivalued fields \nby Mariana Vicaria (Berkeley) as part of Online logic seminar\n\n\nA bstract\nThe model theory of henselian valued fields has been a major topi c of study during the last century. Remarkable work has been achieved by H askell\, Hrushovski and Macpherson to understand the model theory of algeb raically closed valued fields (ACVF). In a sequence of seminal papers they proved that this theory eliminates imaginaries once the geometric sorts a re added and they developed the notion of stable domination\, which descri bes how types over maximally complete bases are controlled by the stable p art of the structure. \n\n I will explain how to extend these results to the broader class of henselian valued fields of equicharacteristic zer o\, residue field algebraically closed and poly- regular value group. This includes many interesting mathematical structures such as the Laurent Ser ies over the Complex numbers\, but more importantly extends the results to valued fields with finitely many definable convex subgroups.\n LOCATION:https://stable.researchseminars.org/talk/OLS/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Valentina Harizanov (George Washington University) DTSTART:20210506T180000Z DTEND:20210506T190000Z DTSTAMP:20260404T111000Z UID:OLS/50 DESCRIPTION:Title: Computability theory and automorphisms of lattices of substructures\nby Valentina Harizanov (George Washington University) as part of Online logic seminar\n\n\nAbstract\nWe use computability-theoretic concepts and methods to study automorphisms of lattices of substructures of a canonical computable infinite-dimensional vector space over the rationals. In parti cular\, we establish the equivalence of the embedding relation for certain automorphism groups with the order relation of the corresponding Turing d egrees. We further determine the Turing degrees of these automorphism grou ps. We establish similar results for the interval Boolean algebra over the rationals. This is joint work with Rumen Dimitrov and Andrei Morozov.\n LOCATION:https://stable.researchseminars.org/talk/OLS/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew Moorhead (University of Kansas) DTSTART:20210520T180000Z DTEND:20210520T190000Z DTSTAMP:20260404T111000Z UID:OLS/51 DESCRIPTION:Title: Higher commutators\, hypercubes\, and the hierarchy of centralizer con ditions\nby Andrew Moorhead (University of Kansas) as part of Online l ogic seminar\n\n\nAbstract\nThe commutator had historically been studied f or specific varieties of algebras until Smith found a general definition f or a commutator that worked for any Mal'cev algebra. Since then the commut ator has become an essential part of the general algebraist's toolkit. Bul atov discovered at the beginning of the century that the (binary) commutat or can be extended to an infinite sequence of higher arity operations\, no one of which are term definable from the others. This discovery has most importantly led to the distinction between a nilpotent algebra and a 'supe rnilpotent' algebra. While this distinction is invisible for groups\, supe rnilpotent Mal'cev algebras share many strong properties with nilpotent gr oups\, while nilpotent algebras need not. We will discuss the extent to wh ich some of the known results of commutator theory can be viewed as a low- dimensional case of a general multidimensional theory.\n LOCATION:https://stable.researchseminars.org/talk/OLS/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Sylvy Anscombe (Université de Paris) DTSTART:20210422T180000Z DTEND:20210422T190000Z DTSTAMP:20260404T111000Z UID:OLS/52 DESCRIPTION:Title: Some existential theories of fields\nby Sylvy Anscombe (Universit é de Paris) as part of Online logic seminar\n\n\nAbstract\nBuilding on pr evious work\, I will discuss Turing reductions between various fragments o f theories of fields. In particular\, we exhibit several theories of field s Turing equivalent to the existential theory of the rational numbers. Thi s is joint work with Arno Fehm.\n LOCATION:https://stable.researchseminars.org/talk/OLS/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrés Villaveces (Universidad Nacional de Colombia) DTSTART:20210513T180000Z DTEND:20210513T190000Z DTSTAMP:20260404T111000Z UID:OLS/53 DESCRIPTION:Title: A partition relation for well-founded trees by Komjáth and Shelah\, a nd two applications to model theory.\nby Andrés Villaveces (Universid ad Nacional de Colombia) as part of Online logic seminar\n\n\nAbstract\nIn 2003\, Komjáth and Shelah proved a partition theorem on scattered order types\; these in turn could be understood as partition relations for class es of well-founded trees. Recently\, two different kinds of applications o f the same partition relation have been used in infinitary logic and in mo del theory: one by Väänänen and Velickovic on games related to Shelah ’s logic $L^1_\\kappa$\, another by Shelah and myself on the “canonica l tree” of an AEC (a generalization of the Scott sentence for an abstrac t elementary class). I will describe the Komjáth-Shelah result in the fir st part and then narrow in the applications (with more details on the seco nd one\, from some recent joint work with Shelah). Time permitting\, I wil l also address a third interaction between partition relations and model t heoretic issues.\n LOCATION:https://stable.researchseminars.org/talk/OLS/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexi Block Gorman (University of Illinois Urbana-Champaign) DTSTART:20210527T180000Z DTEND:20210527T190000Z DTSTAMP:20260404T111000Z UID:OLS/54 DESCRIPTION:Title: Definability on the Reals from Büchi Automata\nby Alexi Block Gor man (University of Illinois Urbana-Champaign) as part of Online logic semi nar\n\n\nAbstract\nBüchi automata are the natural analogue of finite auto mata in the context of infinite strings (indexed by the natural numbers) o n a finite alphabet. We say a subset X of the reals is r-regular if there is a Büchi automaton that accepts (one of) the base-r representations of every element in X\, and rejects the base-r representations of each elemen t in its complement. These sets often exhibit fractal-like behavior—e.g. \, the Cantor set is 3-regular. There are remarkable connections in logic to Büchi automata\, particularly in model theory. In this talk\, I will g ive a characterization of when the expansion of the real ordered additive group by a predicate for a closed r-regular subset of [0\,1] is model-theo retically tame (d-minimal\, NIP\, NTP2). Moreover\, I will discuss how th is coincides with geometric tameness\, namely trivial fractal dimension. This will include a discussion of how the properties of definable sets var y depending on the properties of the Büchi automaton that recognizes the predicate subset.\n LOCATION:https://stable.researchseminars.org/talk/OLS/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Dimitra Chompitaki (University of Crete) DTSTART:20210708T180000Z DTEND:20210708T190000Z DTSTAMP:20260404T111000Z UID:OLS/55 DESCRIPTION:Title: Decidability results of subtheories of commonly used domains in Algebr a and Number Theory\nby Dimitra Chompitaki (University of Crete) as pa rt of Online logic seminar\n\n\nAbstract\nWe will present some known decid ability and undecidability results for theories of the ring-structures of commonly used domains (Polynomial Rings\, Rational Functions\, Formal Powe r Series). Then we will focus on ongoing research relating to some subtheo ries such as: (a) Addition and the Frobenius map for subrings of Rational Functions of positive characteristic\, and (b) Addition and Divisibility f or Formal Power Series. The latter results fall mostly on the "decidabilit y" side: model completeness and elimination of quantifiers.\n LOCATION:https://stable.researchseminars.org/talk/OLS/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Christina Brech (Universidade de São Paulo) DTSTART:20210617T180000Z DTEND:20210617T190000Z DTSTAMP:20260404T111000Z UID:OLS/56 DESCRIPTION:Title: Isomorphic combinatorial families\nby Christina Brech (Universidad e de São Paulo) as part of Online logic seminar\n\n\nAbstract\nWe will re call the notion of compact and hereditary families of finite subsets of so me cardinal κ and their corresponding combinatorial Banach spaces. We pre sent a combinatorial version of Banach-Stone theorem\, which leads natural ly to a notion of isomorphism between families. Our main result shows that different families on ω are not isomorphic\, if we assume them to be spr eading. We also discuss the difference between the countable and the uncou ntable setting. This is a joint work with Claribet Piña.\n LOCATION:https://stable.researchseminars.org/talk/OLS/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Marcelo Arena (Pontificia Universidad Católica de Chile) DTSTART:20210909T180000Z DTEND:20210909T190000Z DTSTAMP:20260404T111000Z UID:OLS/57 DESCRIPTION:Title: Descriptive Complexity for Counting Complexity Classes\nby Marcelo Arena (Pontificia Universidad Católica de Chile) as part of Online logic seminar\n\n\nAbstract\nDescriptive Complexity has been very successful in characterizing complexity classes of decision problems in terms of the pr operties definable in some logics. However\, descriptive complexity for co unting complexity classes\, such as FP and #P\, has not been systematicall y studied\, and it is not as developed as its decision counterpart. In thi s talk\, we will present a framework based on Weighted Logics to address t his issue. Specifically\, by focusing on the natural numbers we obtain a l ogic called Quantitative Second Order Logics (QSO)\, and show how some of its fragments can be used to capture fundamental counting complexity class es such as FP\, #P and FPSPACE\, among others. Moreover\, we use QSO to de fine a hierarchy inside #P\, identifying counting complexity classes with good closure and approximation properties\, and which admit natural comple te problems.\n LOCATION:https://stable.researchseminars.org/talk/OLS/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Joel Nagloo (University of Illinois Chicago) DTSTART:20210819T180000Z DTEND:20210819T190000Z DTSTAMP:20260404T111000Z UID:OLS/58 DESCRIPTION:Title: Geometric triviality in differentially closed fields\nby Joel Nagl oo (University of Illinois Chicago) as part of Online logic seminar\n\n\nA bstract\nIn this talk we revisit the problem of describing the 'finer' str ucture of geometrically trivial strongly minimal sets in $DCF_0$. In parti cular\, I will explain how recent work joint with Guy Casale and James Fre itag on Fuchsian groups (discrete subgroup of $SL_2(\\mathbb{R})$) and aut omorphic functions\, has lead to intriguing questions around the $\\omega$ -categoricity conjecture of Daniel Lascar. This conjecture was disproved i n its full generality by James Freitag and Tom Scanlon using the modular g roup $SL_2(\\mathbb{Z})$ and its automorphic uniformizer (the $j$-function ). I will explain how their counter-example fits into the larger context o f arithmetic Fuchsian groups and has allowed us to 'propose' refinements t o the original conjecture.\n LOCATION:https://stable.researchseminars.org/talk/OLS/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Rachael Alvir (University of Notre Dame) DTSTART:20210610T180000Z DTEND:20210610T190000Z DTSTAMP:20260404T111000Z UID:OLS/60 DESCRIPTION:Title: Scott Complexity and Finitely α-generated Structures\nby Rachael Alvir (University of Notre Dame) as part of Online logic seminar\n\n\nAbst ract\nIn this talk\, we define the notion of a finitely α-generated struc ture and generalize results about Scott sentences earlier known only for f initely generated structures. We will show how these results can be used t o the connect some of the existing non-equivalent definitions of Scott ran k.\n LOCATION:https://stable.researchseminars.org/talk/OLS/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Tarek Sayed-Ahmed (Cairo University) DTSTART:20210603T180000Z DTEND:20210603T190000Z DTSTAMP:20260404T111000Z UID:OLS/61 DESCRIPTION:Title: Atom canonicity\, complete representations\, and omitting types\nb y Tarek Sayed-Ahmed (Cairo University) as part of Online logic seminar\n\n \nAbstract\nClick here for abstract\n LOCATION:https://stable.researchseminars.org/talk/OLS/61/ END:VEVENT BEGIN:VEVENT SUMMARY:Daoud Siniora (American University in Cairo) DTSTART:20210701T180000Z DTEND:20210701T190000Z DTSTAMP:20260404T111000Z UID:OLS/62 DESCRIPTION:Title: Generic automorphisms of homogeneous structures\nby Daoud Siniora (American University in Cairo) as part of Online logic seminar\n\n\nAbstra ct\nAutomorphism groups of countable first-order structures are Polish gro ups under the pointwise convergence topology. An automorphism is called ge neric if its conjugacy class in comeagre. In this talk we focus on generic automorphisms of homogeneous structures\, such structures arise as Fraiss e limits of amalgamation classes of finite structures. We will present joi nt work with Itay Kaplan and Tomasz Rzepecki studying generic automorphism s of the countable universal homogeneous meet-tree.\n LOCATION:https://stable.researchseminars.org/talk/OLS/62/ END:VEVENT BEGIN:VEVENT SUMMARY:Cristobal Rojas (Pontificia Universidad Católica de Chile) DTSTART:20210715T180000Z DTEND:20210715T190000Z DTSTAMP:20260404T111000Z UID:OLS/63 DESCRIPTION:Title: Computability of Harmonic Measure\nby Cristobal Rojas (Pontificia Universidad Católica de Chile) as part of Online logic seminar\n\n\nAbstr act\nAbstract: We will review recent results relating the geometry of a c onnected domain to the computability of its harmonic measure at a given po int x. In particular\, we will discuss examples of domains whose harmonic measure at x is always computable relative to x\, but not uniformly. This construction gives rise to examples of continuous functions arising as sol utions to a Dirichlet problem (so they are even harmonic) which are piecew ise computable (i.e. all their values are computable relative to the input point)\, but not computable.\n LOCATION:https://stable.researchseminars.org/talk/OLS/63/ END:VEVENT BEGIN:VEVENT SUMMARY:Cristina Sernadas (Universidade de Lisbona) DTSTART:20210902T180000Z DTEND:20210902T190000Z DTSTAMP:20260404T111000Z UID:OLS/64 DESCRIPTION:Title: Decidability via Reduction in Logics and Their Combinations\nby Cr istina Sernadas (Universidade de Lisbona) as part of Online logic seminar\ n\n\nAbstract\nDecision problems in logic include semantic based problems like the satisfiability and the validity problems\nand deductive problems like the theoremhood and the consequence problems. Satisfaction systems an d reductions between \nthem are presented as an appropriate context for an alyzing the satisfiability and the validity problems. \nThe notion of re duction is generalized in order to cope with the meet-combination of logic s.\nReductions between satisfaction systems induce reductions between the respective satisfiability problems and (under mild conditions) also betwee n their validity problems. Sufficient conditions are provided for relating satisfiability problems to validity problems. Reflection results for deci dability in the presence of reductions are established. The validity probl em in the meet-combination is proved to be decidable\nwhenever the validi ty problems for the components are decidable. Some examples are discussed \, namely\, the meet-combination of modal logic and intuitionistic logic. Some ongoing work related to consequence problems in the context of conse quence systems and their combination is pointed out. \nThis talk reports o n joint work with João Rasga and Walter Carnielli.\n LOCATION:https://stable.researchseminars.org/talk/OLS/64/ END:VEVENT BEGIN:VEVENT SUMMARY:Hunter Spink (Stanford) DTSTART:20210729T180000Z DTEND:20210729T190000Z DTSTAMP:20260404T111000Z UID:OLS/65 DESCRIPTION:Title: Probabilistic Littlewood-Offord anti-concentration results via model t heory\nby Hunter Spink (Stanford) as part of Online logic seminar\n\n\ nAbstract\nAbstract: (Joint with Jacob Fox and Matthew Kwan) The classical Erdos-Littlewood-Offord theorem says that for any n nonzero vectors in $R ^d$\, a random signed sum concentrates on any point with probability at mo st $O(n^{-1/2})$. Combining tools from probability theory\, additive combi natorics\, and model theory\, we obtain an anti-concentration probability of $n^{-1/2+o(1)}$ for any o-minimal set $S$ in $R^d$ (such as a hypersurf ace defined by a polynomial in $x_1\,...\,x_n\,e^{x_1}\,...\,e^{x_n}$\, or a restricted analytic function) not containing a line segment. We do this by showing such o-minimal sets have no higher-order additive structure\, complementing work by Pila on lower-order additive structure developed to count rational and algebraic points of bounded height.\n LOCATION:https://stable.researchseminars.org/talk/OLS/65/ END:VEVENT BEGIN:VEVENT SUMMARY:Colin Jahel (Université Claude Bernard Lyon 1) DTSTART:20210826T180000Z DTEND:20210826T190000Z DTSTAMP:20260404T111000Z UID:OLS/66 DESCRIPTION:Title: Some progress on the unique ergodicity problem\nby Colin Jahel (Un iversité Claude Bernard Lyon 1) as part of Online logic seminar\n\n\nAbst ract\nIn 2005\, Kechris\, Pestov and Todorcevic exhibited a\ncorrespondenc e between combinatorial properties of structures and\ndynamical properties of their automorphism groups. In 2012\, Angel\,\nKechris and Lyons used t his correspondence to show the unique ergodicity\nof all the minimal actio ns of some subgroups of $S_\\infty$. In this\ntalk\, I will give an overvi ew of the aforementioned results and discuss\nrecent work generalizing res ults of Angel\, Kechris and Lyons in several\ndirections.\n LOCATION:https://stable.researchseminars.org/talk/OLS/66/ END:VEVENT BEGIN:VEVENT SUMMARY:Noah Schweber (Proof School) DTSTART:20210722T180000Z DTEND:20210722T190000Z DTSTAMP:20260404T111000Z UID:OLS/67 DESCRIPTION:Title: Ceers higher up\nby Noah Schweber (Proof School) as part of Online logic seminar\n\n\nAbstract\nAbstract: We examine analogues of ceers (com putably enumerable equivalence relations) in generalized recursion theory - specifically\, in $\\kappa$-recursion theory for $\\kappa$ an uncountabl e regular cardinal. Classically\, the degrees of ceers with respect to com putable embeddability forms a partial order which is maximally complicated \, namely one whose theory is computably isomorphic to that of true arithm etic. We extend this result to the $\\kappa$-ceers. Interestingly\, this r equires a genuinely new argument\, and currently no single approach is kno wn which applies both to $\\omega$ and to uncountable regular $\\kappa$. M oreover\, the situation for singular cardinals\, let alone admissible ordi nals which are not cardinals such as $\\omega_1^{CK}$\, is completely open . If time permits\, we will discuss a second proof of the above result for the special case of $\\kappa=\\omega_1$ which has the advantage of applyi ng to certain generalized computability theories other than $\\kappa$-recu rsion theories.\n\nThis is joint work with Uri Andrews\, Steffen Lempp\, a nd Manat Mustafa.\n LOCATION:https://stable.researchseminars.org/talk/OLS/67/ END:VEVENT BEGIN:VEVENT SUMMARY:Gregory Cherlin (Rutgers University) DTSTART:20211021T180000Z DTEND:20211021T190000Z DTSTAMP:20260404T111000Z UID:OLS/68 DESCRIPTION:Title: Homogeneity and generalized metric spaces\nby Gregory Cherlin (Rut gers University) as part of Online logic seminar\n\n\nAbstract\nGeneralize d metric spaces of various sorts have come up in\nconnection with the stud y of homogeneous structures (classification\,\nRamsey theoretic properties ). I'll discuss examples studied by Sauer\,\nConant\, Braunfeld\, Hubi&cca ron\;ka\, Kone&ccaron\;ný\;\, Ne&scaron\;et&rcaron\;il\, and others. See\, notably\, Kone&ccaron\;ný\;'s master's thesis (arXiv).\n LOCATION:https://stable.researchseminars.org/talk/OLS/68/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexandra Shlapentokh (East Carolina University) DTSTART:20211028T180000Z DTEND:20211028T190000Z DTSTAMP:20260404T111000Z UID:OLS/69 DESCRIPTION:Title: A Mysterious Ring\nby Alexandra Shlapentokh (East Carolina Univers ity) as part of Online logic seminar\n\n\nAbstract\nLet ${\\mathbb Q}^{\\t ext{ab}}$ be the largest abelian extension of $\\mathbb Q$\, or in other w ords the compositum of all cyclotomic extensions. Let $O_{{\\mathbb Q}^{\ \text{ab}}}$ be the ring of integers of ${\\mathbb Q}^{\\text{ab}}$ or the ring of elements of ${\\mathbb Q}^{\\text{ab}}$ satisfying monic irreduci ble polynomials over $\\mathbb Z$. It is not known whether the first-orde r theory of $O_{{\\mathbb Q}^{\\text{ab}}}$ is decidable. ${\\mathbb Q}^{ \\text{ab}}$ is also a degree two extension of a totally real field. Much more is known about the first-order theory of rings of integers of totall y real fields and in some cases one is able to deduce undecidability of th e first-order theory of the ring of integers of a degree 2 extension of a totally real field from an analogous result for the ring of integers of t he totally real field. However this method does not seem to work for ${\\ mathbb Q}^{\\text{ab}}$. We discuss a possible way of resolving this prob lem and some related questions.\n LOCATION:https://stable.researchseminars.org/talk/OLS/69/ END:VEVENT BEGIN:VEVENT SUMMARY:Caroline Terry (Ohio State University) DTSTART:20210916T180000Z DTEND:20210916T190000Z DTSTAMP:20260404T111000Z UID:OLS/70 DESCRIPTION:Title: Speeds of hereditary properties and mutual algebricity\nby Carolin e Terry (Ohio State University) as part of Online logic seminar\n\n\nAbstr act\nA hereditary graph property is a class of finite graphs closed under isomorphism and induced subgraphs. Given a hereditary graph property H\, the speed of H is the function which sends an integer n to the number of d istinct elements in H with underlying set {1\,...\,n}. Not just any funct ion can occur as the speed of hereditary graph property. Specifically\, t here are discrete ``jumps" in the possible speeds. Study of these jumps b egan with work of Scheinerman and Zito in the 90's\, and culminated in a s eries of papers from the 2000's by Balogh\, Bollob\\'{a}s\, and Weinreich\ , in which essentially all possible speeds of a hereditary graph property were characterized. In contrast to this\, many aspects of this problem in the hypergraph setting remained unknown. In this talk we present new hyp ergraph analogues of many of the jumps from the graph setting\, specifical ly those involving the polynomial\, exponential\, and factorial speeds. T he jumps in the factorial range turned out to have surprising connections to the model theoretic notion of mutual algebricity\, which we also discus s. This is joint work with Chris Laskowski.\n LOCATION:https://stable.researchseminars.org/talk/OLS/70/ END:VEVENT BEGIN:VEVENT SUMMARY:Franziska Jahnke (University of Münster) DTSTART:20211014T180000Z DTEND:20211014T190000Z DTSTAMP:20260404T111000Z UID:OLS/71 DESCRIPTION:Title: Decidability and definability in unramified henselian valued fields\nby Franziska Jahnke (University of Münster) as part of Online logic se minar\n\n\nAbstract\nUnramified and finitely ramified henselian valued fie lds are\ncentral to studying model-theoretic phenomena in mixed characteri stic.\nDecidability and definability in unramified henselian valued fields with\nperfect residue field are well understood\, starting with the semin al\nwork of Ax\, Kochen\, and Ershov. In this talk\, we present recent\nde velopments in unramified henselian valued fields with imperfect\nresidue f ield\, and also comment on what changes in the case of finite\nramificatio n. This is joint work with Sylvy Anscombe.\n LOCATION:https://stable.researchseminars.org/talk/OLS/71/ END:VEVENT BEGIN:VEVENT SUMMARY:Sara Uckelman (Durham University) DTSTART:20211118T190000Z DTEND:20211118T200000Z DTSTAMP:20260404T111000Z UID:OLS/72 DESCRIPTION:Title: John Eliot's Logick Primer: A bilingual English-Algonquian logi c textbook\nby Sara Uckelman (Durham University) as part of Online log ic seminar\n\n\nAbstract\nIn 1672 John Eliot\, English Puritan educator an d missionary\, published The Logick Primer: Some Logical Notions to ini tiate the INDIANS in the knowledge of the Rule of Reason\; and to know how to make use thereof [1]. This roughly 80 page pamphlet focuses on in troducing basic syllogistic vocabulary and reasoning so that syllogisms ca n be created from texts in the Psalms\, the gospels\, and other New Testam ent books. The use of logic for proselytizing purposes is not distinctive : What is distinctive about Eliot's book is that it is bilingual\, written in both English and Massachusett\, an Algonquian language spoken in easte rn coastal and southeastern Massachusetts. It is one of the earliest bili ngual logic textbooks\, it is the only textbook that I know of in an indig enous American language\, and it is one of the earliest printed attestatio ns of the Massachusett language.\n\n

In this talk\, I will:\n

\n\n[1] J.[ohn] E.[liot]. The Logick Primer: Some Logical Notions to initiate t he INDIANS in the knowledge of the Rule of Reason\; and to know how to mak e use thereof. Printed by M. J.\, 1672\n LOCATION:https://stable.researchseminars.org/talk/OLS/72/ END:VEVENT BEGIN:VEVENT SUMMARY:Jana Mařiková (Universität Wien) DTSTART:20211111T190000Z DTEND:20211111T200000Z DTSTAMP:20260404T111000Z UID:OLS/73 DESCRIPTION:Title: Definable matchings in o-minimal bipartite graphs\nby Jana Mařiko vá (Universität Wien) as part of Online logic seminar\n\n\nAbstract\nThi s talk will revolve around the question\, under what conditions an o-minim ally definable bipartite graph admits a\ndefinable matching. We discuss s ome context\, a partial result\, and touch on possible applications. This \nis work in progress.\n LOCATION:https://stable.researchseminars.org/talk/OLS/73/ END:VEVENT BEGIN:VEVENT SUMMARY:Natalia García Fritz (Pontificia Universidad Católica de Chile) DTSTART:20211104T180000Z DTEND:20211104T190000Z DTSTAMP:20260404T111000Z UID:OLS/74 DESCRIPTION:Title: Hilbert's tenth problem for rings of exponential polynomials\nby N atalia García Fritz (Pontificia Universidad Católica de Chile) as part o f Online logic seminar\n\n\nAbstract\nAfter being negatively solved by Dav is\, Putnam\, Robinson\, and Matijasevich in 1970\, Hilbert’s tenth prob lem has been extended to a number of other rings. One of the main natural open cases is that of the ring of complex entire functions in one variable . After reviewing some literature around this problem\, in this talk I wil l outline a negative solution of the analogue of Hilbert's tenth problem f or the ring of exponential polynomials\, approaching the case of entire fu nctions. This is joint work with D. Chompitaki\, H. Pasten\, T. Pheidas\, and X. Vidaux.\n LOCATION:https://stable.researchseminars.org/talk/OLS/74/ END:VEVENT BEGIN:VEVENT SUMMARY:Françoise Point (Université de Mons-Hainaut) DTSTART:20211007T180000Z DTEND:20211007T190000Z DTSTAMP:20260404T111000Z UID:OLS/75 DESCRIPTION:Title: Definable groups in topological fields with a generic derivation\n by Françoise Point (Université de Mons-Hainaut) as part of Online logic seminar\n\n\nAbstract\nWe study a class of tame $\\mathcal L$-theories $T$ of topological fields and their extensions by a generic derivation $\\del ta$. The topological fields under consideration include henselian valued f ields of characteristic 0 and real closed fields. We axiomatize the class of the existentially closed $\\mathcal L_\\delta$-expansions.\nWe show tha t $T_\\delta^*$ has $\\mathcal L$-open core (i.e.\, every $\\mathcal L_\\d elta$-definable open set is $\\mathcal L$-definable) and derive both a cel l decomposition theorem and a transfer result of elimination of imaginarie s. Other tame properties of $T$ such as relative elimination of field sort quantifiers\, NIP and distality also transfer to $T_\\delta^*$. \n\\par T hen letting $\\mathcal K$ be a model of $T_\\delta^*$ and $\\mathcal M$ a $\\vert K\\vert^+$-saturated elementary extension of $\\mathcal K$\, we fi rst associate with an $\\mathcal L_\\delta(K)$-definable group $G$ in $\\m athcal M$\, a pro-$\\mathcal L$-definable set $G^{**}_{\\infty}$ in which the differential prolongations $G^{\\nabla_\\infty}$ of elements of $G$ ar e dense\, using the $\\mathcal L$-open core property of $T_\\delta^*$. Fol lowing the same ideas as in the group configuration theorem in o-minimal s tructures as developed by K. Peterzil\, we construct a type $\\mathcal L$- definable topological group $H_\\infty\\subset G^{**}_{\\infty}$\, acting on a $K$-infinitesimal neighbourhood of a generic element of $G^{**}_\\inf ty$ in a faithful\, continuous and transitive way. Further $H_\\infty\\cap G^{\\nabla_\\infty}$ is dense in $H_\\infty$ and the action of $H_\\infty \\cap G^{\\nabla_\\infty}$ coincides with the one induced by the initial $ \\mathcal L_\\delta$-group action. \n\\par The first part of this work is joint with Pablo Cubid\\`es Kovacsics.\n LOCATION:https://stable.researchseminars.org/talk/OLS/75/ END:VEVENT BEGIN:VEVENT SUMMARY:Vasco Brattka (Universität der Bundeswehr München) DTSTART:20211202T190000Z DTEND:20211202T200000Z DTSTAMP:20260404T111000Z UID:OLS/77 DESCRIPTION:Title: A Galois connection between Turing jumps and limits\nby Vasco Brat tka (Universität der Bundeswehr München) as part of Online logic seminar \n\n\nAbstract\nWe discuss a Galois connection between Turing jumps and li mits\nthat offers a fresh view on the class of limit computable functions\ nand its properties. This view does not only offer simplified proofs\nof m any known classical results in computable analysis\, but also\nnew insight s. With this approach we also propagate a more uniform\nview on computabil ity theory in general.\n LOCATION:https://stable.researchseminars.org/talk/OLS/77/ END:VEVENT BEGIN:VEVENT SUMMARY:Gihanee Senadheera (Southern Illinois University) DTSTART:20210930T180000Z DTEND:20210930T190000Z DTSTAMP:20260404T111000Z UID:OLS/78 DESCRIPTION:Title: Effective Concept Classes of PACi/PAC Incomparable Degrees and Jump St ructure\nby Gihanee Senadheera (Southern Illinois University) as part of Online logic seminar\n\n\nAbstract\nThe Probably Approximately Correct (PAC) learning is a machine learning model introduced by Leslie Valiant in 1984. The PACi reducibility refers to the PAC reducibility independent of size and computation time. This reducibility in PAC learning resembles th e reducibility in Turing computability. In 1957 Friedberg and Muchnik inde pendently solved the Post problem by constructing computably enumerable se ts $A$ and $B$ of incomparable degrees using the priority construction met hod. We adapt this idea to PACi/PAC reducibilities and construct two the e ffective concept classes $C_0$ and $C_1$ such that $C_0$ is not reducible to $C_1$ and vice versa. When considering PAC reducibility it was necessar y to work on the size of an effective concept class\, thus we use Kolmogor ov complexity to obtain the size. Analogous to Turing jump\, we give a jum p structure on effective concept classes. As the future work\, we begin to explore an embedding of structures from PAC degrees to 1-1 degrees or Tur ing degrees.\n LOCATION:https://stable.researchseminars.org/talk/OLS/78/ END:VEVENT BEGIN:VEVENT SUMMARY:Mostafa Mirabi (Wesleyan University) DTSTART:20211209T190000Z DTEND:20211209T200000Z DTSTAMP:20260404T111000Z UID:OLS/79 DESCRIPTION:Title: MS-measurability via Coordinatization\nby Mostafa Mirabi (Wesleyan University) as part of Online logic seminar\n\n\nAbstract\nAbstract: In t his talk\, we first discuss the concept of MS-measurable structures\, intr oduced by Macpherson and Steinhorn in 2007. Then we will define a strong n otion of Coordinatization for $\\aleph_0$-categorical structures and show that a structure which is coordinatized by $\\aleph_0$-categorical MS-meas urable structures itself is MS-measurable. This approach provides a way to build new MS-measurable structures.\n LOCATION:https://stable.researchseminars.org/talk/OLS/79/ END:VEVENT BEGIN:VEVENT SUMMARY:Todor Tsankov (Institut Camille Jordan) DTSTART:20211216T190000Z DTEND:20211216T200000Z DTSTAMP:20260404T111000Z UID:OLS/80 DESCRIPTION:Title: Continuous logic and Borel equivalence relations\nby Todor Tsankov (Institut Camille Jordan) as part of Online logic seminar\n\n\nAbstract\n The theory of Borel reducibility of definable equivalence relations\nwas i nitiated by Friedman and Stanley who were specifically interested\nin the equivalence relation of isomorphism of countable structures.\nSince then\, the scope of the theory has considerably expanded but\nisomorphism of cou ntable structures remains one of the situations\nwhere the most detailed r esults are available and where both methods of\ninfinitary model theory an d descriptive set theory can be applied. In\nthis talk\, I will explain ho w infinitary continuous logic can be used\nto extend parts of this theory to metric structures. Our main result\nis about isomorphism of locally com pact metric structures and it is\na common generalization of theorems of H jorth (for locally compact\nmetric spaces) and Hjorth and Kechris (for cou ntable structures). This\nis joint work with Andreas Hallbä\;ck and Ma ciej Malicki.\n LOCATION:https://stable.researchseminars.org/talk/OLS/80/ END:VEVENT BEGIN:VEVENT SUMMARY:Lauren Wickman (University of Florida) DTSTART:20220127T190000Z DTEND:20220127T200000Z DTSTAMP:20260404T111000Z UID:OLS/81 DESCRIPTION:Title: Knaster Continua and Projective Fraïssé Theory\nby Lauren Wickma n (University of Florida) as part of Online logic seminar\n\n\nAbstract\nT he Knaster continuum\, also known as the buckethandle\, or the Brouwer–J aniszewski–Knaster continuum can be viewed as an inverse limit of 2-tent maps on the interval. However\, there is a whole class (with continuum ma ny non-homeomorphic members) of Knaster continua\, each viewed as an inver se limit of p-tent maps\, where p is a sequence of primes. In this talk\, for each Knaster continuum K\, we will give a projective Fraïssé class o f finite objects that approximate K (up to homeomorphism) and examine the combinatorial properties of that the class (namely whether the class is Ra msey or if it has a Ramsey extension). We will give an extremely amenable subgroup of the homeomorphism group of the universal Knaster continuum.\n LOCATION:https://stable.researchseminars.org/talk/OLS/81/ END:VEVENT BEGIN:VEVENT SUMMARY:Caleb Camrud (Iowa State University) DTSTART:20220113T190000Z DTEND:20220113T200000Z DTSTAMP:20260404T111000Z UID:OLS/82 DESCRIPTION:Title: Continuous Logic\, Diagrams\, and Truth Values for Computable Presenta tions\nby Caleb Camrud (Iowa State University) as part of Online logic seminar\n\n\nAbstract\nGoldbring\,McNicholl\, and I investigated the arit hmetic and hyperarithmetic degrees of the finitary and computable infinita ry diagrams of continuous logic for computably presented metric structures . As the truth value of a sentence of continuous logic may be any real in [0\,1]\, we introduced two kinds of diagrams at each level: the closed dia gram\, which encapsulates weak inequalities of truth values\, and the open diagram\, which encapsulates strict inequalities. We showed that\, for an y computably presented metric structure and any computable ordinal $\\alph a$\, the closed and open $\\Sigma^c_\\alpha$ diagrams are $\\Pi^0_{\\alpha +1}$ and $\\Sigma^0_\\alpha$\, respectively\, and that the closed and open $\\Pi^c_\\alpha$ diagrams are $\\Pi^0_\\alpha$ and $\\Sigma^0_{\\alpha+1} $.\n\nProving the optimality of these bounds\, however\, was non-trivial. Since the standard presentation of [0\,1] with the Euclidean metric is com putably compact\, we were forced to work on the natural numbers with the d iscrete metric (in some sense\, the "simplest" non-compact metric space). Along the way\, we also proved some surprising combinatorial results. McNi choll and I then continued our study of computable infinitary continuous l ogic and found that for any nonzero computable ordinal $\\alpha$ and any r ight $\\Pi^0_\\alpha$ (or $\\Sigma^0_\\alpha$) real number\, there is a $\ \Pi^c_\\alpha$ (or $\\Sigma^c_\\alpha$) sentence which is universally inte rpreted as that value.\n LOCATION:https://stable.researchseminars.org/talk/OLS/82/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Turetsky (Victoria University of Wellington) DTSTART:20220120T190000Z DTEND:20220120T200000Z DTSTAMP:20260404T111000Z UID:OLS/83 DESCRIPTION:Title: True Stages -- From Priority Arguments to Descriptive Set Theory\n by Daniel Turetsky (Victoria University of Wellington) as part of Online l ogic seminar\n\n\nAbstract\nThe true stages machinery was conceived as a t echnique for organizing complex priority constructions in computability th eory\, much like Ash's metatheorem. With a little modification\, however\ , it can prove remarkably useful in descriptive set theory. Using this ma chinery\, we can obtain nice proofs of results of Wadge\, Hausdorff and Ku ratowski\, and Louveau\, sometimes strengthening the result in the process .\nWithout getting too deep into the details\, I will give the ideas of th e machinery and how it applies to descriptive set theory.\n LOCATION:https://stable.researchseminars.org/talk/OLS/83/ END:VEVENT BEGIN:VEVENT SUMMARY:Roman Kossak (Graduate Center\, City University of New York) DTSTART:20220224T190000Z DTEND:20220224T200000Z DTSTAMP:20260404T111000Z UID:OLS/84 DESCRIPTION:Title: Undefinability and absolute undefinability in models of arithmetic \nby Roman Kossak (Graduate Center\, City University of New York) as part of Online logic seminar\n\n\nAbstract\nI will survey some well-known and s ome more recent undefinability results about models of Peano Arithmetic. I want to contrast first-order undefinability in the standard model with a much stronger notion of undefinability which is suitable for resplendent models\, and use the results to motivate some more general questions about the nature of undefinability.\n LOCATION:https://stable.researchseminars.org/talk/OLS/84/ END:VEVENT BEGIN:VEVENT SUMMARY:Adam Case (Drake University) DTSTART:20220303T190000Z DTEND:20220303T200000Z DTSTAMP:20260404T111000Z UID:OLS/85 DESCRIPTION:Title: Finite-State Mutual Dimension\nby Adam Case (Drake University) as part of Online logic seminar\n\n\nAbstract\nIn this talk\, I will discuss recent work with Jack H. Lutz on a notion of finite-state mutual dimension . Intuitively\, the finite-state dimension of a sequence S represents the density of finite-state information contained within S\, while the finite- state mutual dimension between two sequences S and T represents the densit y of finite-state information shared by S and T. Thus "finite-state mutual dimension" can be viewed as a "finite-state" version of mutual dimension and as a "mutual" version of finite-state dimension. The main results that will be discussed are as follows. First\, we show that finite-state mutua l dimension\, defined using information-lossless finite-state compressors\ , has all of the properties expected of a measure of mutual information. N ext\, we prove that finite-state mutual dimension may be characterized in terms of block mutual information rates. Finally\, we provide necessary an d sufficient conditions for two normal sequences to achieve finite-state m utual dimension zero.\n LOCATION:https://stable.researchseminars.org/talk/OLS/85/ END:VEVENT BEGIN:VEVENT SUMMARY:Antonina Kolokolova (Memorial University of Newfoundland) DTSTART:20220210T190000Z DTEND:20220210T200000Z DTSTAMP:20260404T111000Z UID:OLS/86 DESCRIPTION:Title: Learning from bounded arithmetic\nby Antonina Kolokolova (Memorial University of Newfoundland) as part of Online logic seminar\n\n\nAbstract \nThe central question of complexity theory -- what can (and cannot) be fe asibly computed -- has a corresponding logical meta-question: what can (a nd cannot) be feasibly proven. While complexity theory studies the former \, bounded arithmetic is one of the main approaches to the meta-question. There is a tight relation between theories of bounded arithmetic and corre sponding complexity classes\, allowing one to study what can be proven in\ , for example\, "polynomial-time reasoning" and what power is needed to re solve complexity questions\, with a number of both positive and negative p rovability results.\n\nHere\, we focus on the complexity of another meta-p roblem: learning to solve problems such as Boolean satisfiability. There i s a range of ways to define "solving problems"\, with one extreme\, the un iform setting\, being an existence of a fast algorithm (potentially rando mized)\, and another of a potentially non-computable family of small Boole an circuits\, one for each problem size. The complexity of learning can b e recast as the complexity of finding a procedure to generate Boolean circ uits solving the problem of a given size\, if it (and such a family of cir cuits) exists.\n\nFirst\, inspired by the KPT witnessing theorem\, a spec ial case of Herbrand's theorem in bounded arithmetic\, we develop an inter mediate notion of uniformity that we call LEARN-uniformity. While non-uni form lower bounds are notoriously difficult\, we can prove several uncondi tional lower bounds for this weaker notion of uniformity. Then\, returnin g to the world of bounded arithmetic and using that notion of uniformity a s a tool\, we show unprovability of several complexity upper bounds for bo th deterministic and randomized complexity classes\, in particular giving simpler proofs that the theory of polynomial-time reasoning PV does not pr ove that all of P is computable by circuits of a specific polynomial size\ , and the theory $V^1$\, a second-order counterpart to the classic Buss' t heory $S^1_2$\, does not prove the same statement with NP instead of P. \ n\nFinally\, we leverage these ideas to show that bounded arithmetic "has trouble differentiating" between uniform and non-uniform frameworks: more specifically\, we show that theories for polynomial-time and randomized polynomial-time reasoning cannot prove both a uniform lower bound and a n on-uniform upper bound for NP. In particular\, while it is possible that NP != P yet all of NP is computable by families of polynomial-size circui ts\, this cannot be proven feasibly.\n LOCATION:https://stable.researchseminars.org/talk/OLS/86/ END:VEVENT BEGIN:VEVENT SUMMARY:John Baldwin (University of Illinois\, Chicago) DTSTART:20220317T180000Z DTEND:20220317T190000Z DTSTAMP:20260404T111000Z UID:OLS/87 DESCRIPTION:Title: Category theory and Model Theory: Symbiotic Scaffolds\nby John Bal dwin (University of Illinois\, Chicago) as part of Online logic seminar\n\ n\nAbstract\nA scaffold for mathematics includes both local foundations for\nvarious areas of mathematics and productive guidance in h ow to unify them. In\na scaffold the unification does not take place by a common axiomatic basis\nbut consists of a systematic ways of connecting re sults and proofs in various\nareas of mathematics. Two scaffolds\, model theory and category theory\,\nprovide local foundations for many areas of mathematic including two flavors\n(material and structural) of set theory and different approaches to\nunification. We will discuss salient feature s of the two scaffolds including\ntheir contrasting but bi-interpretable s et theories. We focus on the\ncontrasting treatments of `size' in each sca ffold and the\n advantages/disadvantages of each for different proble ms.\n LOCATION:https://stable.researchseminars.org/talk/OLS/87/ END:VEVENT BEGIN:VEVENT SUMMARY:George Metcalfe (University of Bern) DTSTART:20220428T180000Z DTEND:20220428T190000Z DTSTAMP:20260404T111000Z UID:OLS/88 DESCRIPTION:Title: From ordered groups to ordered monoids and back again\nby George M etcalfe (University of Bern) as part of Online logic seminar\n\n\nAbstract \n(Joint work with Almudena Colacito\, Nikolaos Galatos\, and Simon Santsc hi)\n\nRemoving the inverse operation from any lattice-ordered group (l-gr oup)\, such as the ordered additive group of integers\, produces a distrib utive lattice-ordered monoid (l-monoid)\, but it is not the case that ever y distributive l-monoid admits a group structure. In particular\, every l- group embeds into an l-group of automorphisms of some chain and is either trivial or infinite\, whereas every distributive l-monoid embeds into a po ssibly finite l-monoid of endomorphisms of some chain.\n\nIn this talk\, w e will see that inverse-free abelian l-groups generate only a proper (infi nitely based) subvariety of the variety of commutative distributive l-mono ids\, but inverse-free l-groups generate the whole variety of distributive l-monoids. We will also see that the validity of an l-group equation can be reduced to the validity of a (constructible) finite set of l-monoid equ ations\, yielding --- since the variety of distributive l-monoids has the finite model property — an alternative proof of the decidability of the equational theory of l-groups.\n LOCATION:https://stable.researchseminars.org/talk/OLS/88/ END:VEVENT BEGIN:VEVENT SUMMARY:Riley Thornton (UCLA) DTSTART:20220324T180000Z DTEND:20220324T190000Z DTSTAMP:20260404T111000Z UID:OLS/89 DESCRIPTION:Title: An algebraic approach to Borel CSPs\nby Riley Thornton (UCLA) as p art of Online logic seminar\n\n\nAbstract\nI will explain how some of the algebraic tools behind the CSP dichotomy theorem in computer science can b e adapted to answer questions in Borel combinatorics.\n LOCATION:https://stable.researchseminars.org/talk/OLS/89/ END:VEVENT BEGIN:VEVENT SUMMARY:Manlio Valenti (University of Udine) DTSTART:20220331T180000Z DTEND:20220331T190000Z DTSTAMP:20260404T111000Z UID:OLS/90 DESCRIPTION:Title: The first-order part of Weihrauch degrees\nby Manlio Valenti (Univ ersity of Udine) as part of Online logic seminar\n\n\nAbstract\nGiven an o rder $(P\,\\le)$\, a natural strategy to prove that $a \\not\\le b$ is to present an example of some $c\\le a$ such that $c \\not\\le b$. Of course\ , choosing such a $c$ can be very challenging.\n\nIn the context of TTE an d Weihrauch reducibility\, (Dzhafarov\, Solomon\, Yokoyama) introduced the notion of ``first-order part" of a computational problem $f$\, capturing the ``strongest computational problem that is Weihrauch-below $f$". Charac terizing the first-order part of a given problem can be challenging as wel l\, but it proved to be a very useful tool\, especially when comparing pri nciples that are (relatively) high in the Weihrauch hierarchy.\n\nIn this talk\, we will study the first-order part from a more algebraic perspectiv e\, and study its relation with several other operators already defined in the literature. We will then show how the obtained results can be used to easily characterize the first-order part of many known problems.\n LOCATION:https://stable.researchseminars.org/talk/OLS/90/ END:VEVENT BEGIN:VEVENT SUMMARY:Forte Shinko (Cal Tech) DTSTART:20220414T180000Z DTEND:20220414T190000Z DTSTAMP:20260404T111000Z UID:OLS/92 DESCRIPTION:Title: Realizations of equivalence relations and subshifts\nby Forte Shin ko (Cal Tech) as part of Online logic seminar\n\n\nAbstract\nEvery continu ous action of a countable group on a Polish space induces a Borel equivale nce relation. We are interested in the problem of realizing (i.e. finding a Borel isomorphic copy of) these equivalence relations as continuous acti ons on compact spaces. We provide a number of positive results for variant s of this problem\, and we investigate the connection to subshifts.\n LOCATION:https://stable.researchseminars.org/talk/OLS/92/ END:VEVENT BEGIN:VEVENT SUMMARY:Ioannis Souldatos (Aristotle University of Thessaloniki) DTSTART:20220505T180000Z DTEND:20220505T190000Z DTSTAMP:20260404T111000Z UID:OLS/93 DESCRIPTION:Title: (Non)-Absolute Characterizations of Cardinals\nby Ioannis Souldato s (Aristotle University of Thessaloniki) as part of Online logic seminar\n \n\nAbstract\nPDF Abstract Here\n LOCATION:https://stable.researchseminars.org/talk/OLS/93/ END:VEVENT BEGIN:VEVENT SUMMARY:Francesca Zaffora Blando (Carnegie Mellon University) DTSTART:20221215T190000Z DTEND:20221215T200000Z DTSTAMP:20260404T111000Z UID:OLS/94 DESCRIPTION:Title: Randomness and Invariance\nby Francesca Zaffora Blando (Carnegie M ellon University) as part of Online logic seminar\n\n\nAbstract\nThe first (semi-)formal definition of randomness for infinite binary sequences date s back to von Mises’ work in the foundations of probability and sta tistics. According to von Mises\, a sequence is random if\, within it\, th e relative frequencies of 0 and 1 converge to a limit and these limiting r elative frequencies are invariant under a class of transformations called selection rules. The randomness notion introduced by von Mises is nowadays widely regarded as being too weak and his account has been supplanted by the theory of algorithmic randomness\, which characterizes randomness usin g the tools of computability theory and measure theory. The goal of this t alk is two-fold. First\, I will discuss a lesser-known characterization of Schnorr randomness due to Schnorr\, which demonstrates that it is possibl e to obtain a satisfactory randomness notion by defining randomness\, anal ogously to how von Mises did it\, in terms of the invariance of limiting r elative frequencies. Then\, I will discuss how other canonical algorithmic randomness notions are similarly characterizable in terms of the preserva tion of natural properties under the class of computable measure-preservin g transformations. This talk is based on joint work with Floris Persiau.\n LOCATION:https://stable.researchseminars.org/talk/OLS/94/ END:VEVENT BEGIN:VEVENT SUMMARY:Ramyaa (New Mexico Tech) DTSTART:20220818T180000Z DTEND:20220818T190000Z DTSTAMP:20260404T111000Z UID:OLS/95 DESCRIPTION:Title: Advances in Differentiable Program Learning\nby Ramyaa (New Mexico Tech) as part of Online logic seminar\n\n\nAbstract\nInductive Logic Prog ramming (ILP) is a subfield of Artificial Intelligence that learns Logic P rograms for a concept from positive and negative examples of the concept.\ nLearning Logic Programs allow for interpretability\, can benefit from bac kground knowledge\, and require small training set. However\, traditional ILP techniques are not noise-tolerant\, and do not scale well to large/hig h-dimensional domains. In recent years\, there have been several attempts to use differentiable representations of logic programs and learn them usi ng gradient descent based techniques. This talk introduces these attempts\ , and our efforts at extending them to learn logic programs with negations and higher-order logic programs.\n\nIn both cases\, considerable care is needed from a theoretical standpoint. Negation should be restricted to avo id paradoxical scenarios. We learned logic programs with stratified negati on (in the style of Datalog). Anti-unification (i.e.\, generalization) of arbitrary higher-order terms is not unique. We learned second order logic programs that are generalizations of first order programs.\n LOCATION:https://stable.researchseminars.org/talk/OLS/95/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabriel Conant (The Ohio State University) DTSTART:20221027T180000Z DTEND:20221027T190000Z DTSTAMP:20260404T111000Z UID:OLS/96 DESCRIPTION:Title: Separation for isometric group actions and hyperimaginary independence \nby Gabriel Conant (The Ohio State University) as part of Online logi c seminar\n\n\nAbstract\nIn the theory of (finite) permutation groups\, P. M. Neumann’s Lemma says that if a group G acts on a set X\, and P is a finite subset of X such that all points of P have an infinite orbit\, then for any other finite set in Q there is a group element g such that gP is disjoint from Q. When applied to the automorphism group of a first-order s tructure\, this lemma can be used to prove a number of useful results in m odel theory. In this talk\, I will present a metric space version of P. M. Neumman’s Lemma\, along with several applications in the model theory o f metric structures. For example\, we show that algebraic independence in continuous logic satisfies the “full existence axiom”\, answering a qu estion of Andrews\, Goldbring\, and Keisler. Time permitting\, I will also discuss some consequences for hyperimaginaries\, which are new even in cl assical discrete logic. Joint work with J. Hanson.\n LOCATION:https://stable.researchseminars.org/talk/OLS/96/ END:VEVENT BEGIN:VEVENT SUMMARY:Xavier Vidaux (Universidad de Concepción) DTSTART:20220825T180000Z DTEND:20220825T190000Z DTSTAMP:20260404T111000Z UID:OLS/97 DESCRIPTION:Title: Towers of totally real nested square roots: undecidability\, the latti ce of subfields\, and the quartic extensions within the tower\nby Xavi er Vidaux (Universidad de Concepción) as part of Online logic seminar\n\n \nAbstract\nAfter recalling some first order undecidability results in inf inite algebraic extensions of the field of rational numbers\, I will talk about a concrete family of 2-towers of totally real number fields\, namely \, $(\\mathbb{Q}(x_n))_{n\\ge0}$\, where $x_{n+1}=\\sqrt{\\nu+x_n}$ for so me given positive integers $\\nu$ and $x_0$. Let $K$ be the union of the $ \\mathbb{Q}(x_n)$. Though these fields $K$ are somewhat the simplest subfi elds of an algebraic closure of $\\mathbb{Q}$ that one may construct\, the y hide a rich variety of natural problems of topological\, algebraic\, dyn amical and logical nature. The results that I will present about these fie lds are due to M. Castillo\, C. Videla\, and who writes.\n LOCATION:https://stable.researchseminars.org/talk/OLS/97/ END:VEVENT BEGIN:VEVENT SUMMARY:Karen Lange (Wellesley College) DTSTART:20220901T180000Z DTEND:20220901T190000Z DTSTAMP:20260404T111000Z UID:OLS/99 DESCRIPTION:Title: Classification via effective lists\nby Karen Lange (Wellesley Coll ege) as part of Online logic seminar\n\n\nAbstract\n"Classifying" a natura l class of structures is a common goal in mathematics. Providing a class ification can mean different things\, e.g.\, determining a set of invarian ts that settle the isomorphism problem or instead creating a list of all s tructures of a given kind without repetition of isomorphism type. Here we discuss recent work on classifications of the latter kind from the perspec tive of computable structure theory. We’ll consider natural classes of computable structures such as vector spaces\, equivalence relations\, alg ebraic fields\, and trees to better understand the nuances of classificati on via effective lists and its relationship to other forms of classificati on.\n LOCATION:https://stable.researchseminars.org/talk/OLS/99/ END:VEVENT BEGIN:VEVENT SUMMARY:Patricia Blanchette (University of Notre Dame) DTSTART:20220908T180000Z DTEND:20220908T190000Z DTSTAMP:20260404T111000Z UID:OLS/100 DESCRIPTION:Title: Formalism in Logic\nby Patricia Blanchette (University of Notre D ame) as part of Online logic seminar\n\n\nAbstract\nLogic became ‘formal ’ at the end of the 19th century primarily in pursuit of deductive rigor within mathematics. But by the early 20th century\, a formal treatment of logic had become essential to two new streams in the current of logic: th e collection of crucial ‘semantic’ notions surrounding the idea of cat egoricity\, and the project of examining the tools of logic themselves\, i n the way that’s crucial for the treatment of completeness (in its vario us guises). This lecture discusses the variety of different tasks that hav e been assigned the notion of formalization in the recent history of logic \, with an emphasis on some of the ways in which the distinct purposes of formalization are not always in harmony with one another.\n LOCATION:https://stable.researchseminars.org/talk/OLS/100/ END:VEVENT BEGIN:VEVENT SUMMARY:Neer Bhardwaj (Weizmann Institute) DTSTART:20220915T180000Z DTEND:20220915T190000Z DTSTAMP:20260404T111000Z UID:OLS/101 DESCRIPTION:Title: An analytic AKE program with induced structure results on coefficient field and monomial group\nby Neer Bhardwaj (Weizmann Institute) as pa rt of Online logic seminar\n\n\nAbstract\nWe develop an extension theory f or analytic valuation rings in order to establish Ax-Kochen-Ersov type res ults for these structures. New is that we can add in salient cases lifts o f the residue field and the value group and show that the induced structur e on the lifted residue field is just its field structure\, and on the lif ted value group is just its ordered abelian group structure. This restores an analogy with the non-analytic AKE-setting that was missing in earlier treatments of analytic AKE-theory. Joint work with Lou van den Dries.\n LOCATION:https://stable.researchseminars.org/talk/OLS/101/ END:VEVENT BEGIN:VEVENT SUMMARY:Philip White (George Washington University) DTSTART:20221103T180000Z DTEND:20221103T190000Z DTSTAMP:20260404T111000Z UID:OLS/102 DESCRIPTION:Title: A Two-Cardinal Ramsey Operator on Ideals\nby Philip White (George Washington University) as part of Online logic seminar\n\n\nAbstract\nLet $I$ be a $\\kappa$-complete ideal on $\\kappa$. Similar to the one-cardin al ineffability operator of Baumgartner\, Feng defined a one-cardinal Rams ey operator on $I$. A basic result of Feng is applying the one cardinal Ra msey operator to $I$ yields a normal ideal. Feng also showed under what co nditions the ideal given by applying the Ramsey operator is equivalently g enerated by a “pre-Ramsey” ideal as well as the $\\Pi^1_{n+1}$ indescr ibability ideal. Finally Feng showed iterated use of the one-cardinal Ram sey operator forms a proper hierarchy. Feng was able to show these results for $< \\kappa+$ iterations of the one-cardinal Ramsey operator by utiliz ing canonical functions. Similar to other results of Brent Cody and the pr esenter\, these results in the one-cardinal setting can be generalized to a two-cardinal setting. The theorems of Feng will be discussed in detail a s well as the analogous two-cardinal versions of Brent Cody and the presen ter.\n LOCATION:https://stable.researchseminars.org/talk/OLS/102/ END:VEVENT BEGIN:VEVENT SUMMARY:Jonathan Protzenko (Microsoft Research) DTSTART:20221013T180000Z DTEND:20221013T190000Z DTSTAMP:20260404T111000Z UID:OLS/103 DESCRIPTION:Title: Computational Law: Programming Languages meet the Law\nby Jonatha n Protzenko (Microsoft Research) as part of Online logic seminar\n\n\nAbst ract\nMany parts of the law\, such as tax code\, pension computations\, et c. encode a clear and unambiguous algorithm: they are called computational law. But ordinary citizens without legal counsel are oftentimes powerless \, because layers of legalese and opaque implementations obscure the under lying algorithm.\n\nThe Correct Computational Law project tackles this ine quity by formalizing and capturing computational law using formal methods. Whether it is the French Tax Code\, French family benefits or Washington State's Legal Financial Obligations\, we formalize\, re-implement and find bugs in the law. Doing so\, we make it possible for ordinary citizens to prevail over the complexity of the law\, rather than falling prey to it.\n \nWe will first describe our research agenda and ongoing efforts spanning France and the US. Then\, we will focus on a case study: the complexity of federal civil procedure in the US\, and how the Lean proof assistant can always find\, with mathematical certainty\, a path through the pleading ph ase that fulfills all major procedural requirements.\n LOCATION:https://stable.researchseminars.org/talk/OLS/103/ END:VEVENT BEGIN:VEVENT SUMMARY:Kirsten Eisenträger (Penn State University) DTSTART:20221020T180000Z DTEND:20221020T190000Z DTSTAMP:20260404T111000Z UID:OLS/104 DESCRIPTION:Title: A topological approach to undefinability in algebraic extensions of t he rationals\nby Kirsten Eisenträger (Penn State University) as part of Online logic seminar\n\n\nAbstract\nIn 1970 Matiyasevich proved that Hi lbert’s Tenth Problem over the\nintegers is undecidable\, building on wo rk by Davis-Putnam-Robinson.\nHilbert’s Tenth Problem over the rationals is still open\, but it could\nbe resolved by giving an existential defini tion of the integers inside\nthe rationals.\n\nProving whether such a defi nition exists is still out of reach. However\,\nwe will show that only “ very few” algebraic extensions of the rationals\nhave the property that their ring of integers are existentially or\nuniversally definable. Equipp ing the set of all algebraic extensions of\nthe rationals with a natural t opology\, we show that only a meager subset\nhas this property. An import ant tool is a new normal form theorem for\nexistential definitions in such extensions. As a corollary\, we\nconstruct countably many distinct compu table algebraic extensions whose\nrings of integers are neither existentia lly nor universally definable.\nJoint work with Russell Miller\, Caleb Spr inger\, and Linda Westrick.\n LOCATION:https://stable.researchseminars.org/talk/OLS/104/ END:VEVENT BEGIN:VEVENT SUMMARY:Hunter Spink (Stanford University) DTSTART:20220922T180000Z DTEND:20220922T190000Z DTSTAMP:20260404T111000Z UID:OLS/105 DESCRIPTION:Title: Random walks and combinatorial dimensions in o-minimal groups\nby Hunter Spink (Stanford University) as part of Online logic seminar\n\n\nA bstract\nI will discuss some ideas that go into showing that $n$-independe nt-step random walks in o-minimally definable group over the real numbers (like a semi-algebraic group) has at most an $n^{-C}$ probability of finis hing on a lower-dimensional target set unless the target set contains an ` `exponential arc''\, where $C$ only depends on the dimension of the target set.\n LOCATION:https://stable.researchseminars.org/talk/OLS/105/ END:VEVENT BEGIN:VEVENT SUMMARY:Vincent Bagayoko (Université de Mons) DTSTART:20221110T190000Z DTEND:20221110T200000Z DTSTAMP:20260404T111000Z UID:OLS/106 DESCRIPTION:Title: Some ordered groups of generalized series\nby Vincent Bagayoko (U niversité de Mons) as part of Online logic seminar\n\n\nAbstract\nI will talk about some problems relating linearly ordered groups to logic and rea l geometry.\nI will show how to certain generalized series\, similar to tr ansseries\, in order to answer an open question regarding orderable groups .\n LOCATION:https://stable.researchseminars.org/talk/OLS/106/ END:VEVENT BEGIN:VEVENT SUMMARY:Barbara Csima (University of Waterloo) DTSTART:20221117T190000Z DTEND:20221117T200000Z DTSTAMP:20260404T111000Z UID:OLS/107 DESCRIPTION:Title: Degrees of Categoricity\nby Barbara Csima (University of Waterloo ) as part of Online logic seminar\n\n\nAbstract\nA degree of categoricity is a Turing degree that exactly captures the complexity of computing isomo rphisms between computable copies of some computable structure. In this ta lk I will start by giving some easy examples of degrees of categoricity. I will then give a review of what is known about degrees of categoricity\, culminating in new results (joint work with Dino Rossegger).\n LOCATION:https://stable.researchseminars.org/talk/OLS/107/ END:VEVENT BEGIN:VEVENT SUMMARY:David Schrittesser (University of Toronto) DTSTART:20221201T190000Z DTEND:20221201T200000Z DTSTAMP:20260404T111000Z UID:OLS/108 DESCRIPTION:Title: Nonstandard analysis and statistical decision theory\nby David Sc hrittesser (University of Toronto) as part of Online logic seminar\n\n\nAb stract\nStatistical decision theory takes inspiration from game theory to provide a basic framework in which one can reason about optimality (or lac k thereof) of statistical procedures\, such as estimators and tests.\n\nOn e property of a statistical procedure is "admissibility": Roughly\, a proc edure is admissible if there is no other procedure which does better under all circumstances ("better" in a sense specified by the decision theoreti cal framework\, i.e.\, with respect to a fixed loss function). This is cer tainly a necessary condition for optimality.\n\nAdmissibility is notorious ly hard to characterize. In particular\, establishing a characterization i n Bayesian terms has been an ongoing pursuit for decades in statistical de cision theory. Recently we have found a characterization of admissibility in Bayesian terms\, by using prior probability distributions which can tak e on infinitesimal values. We are also able to draw connections to classic al methods establishing admissibility\, such as Blyth's method and Stein's characterization of admissibility (which does partially characterize admi ssibility\, but only under additional\, technical hypotheses). Finally\, o ur method has applications in concrete problems such as the problem of est ablishing the admissibility of the Graybill-Deal estimator.\n\nThe talk wi ll not presuppose any knowledge on statistics or nonstandard analysis. Eve rything is joint work with D. Roy and H. Duanmu.\n LOCATION:https://stable.researchseminars.org/talk/OLS/108/ END:VEVENT BEGIN:VEVENT SUMMARY:Patrick Lutz (UCLA) DTSTART:20230119T190000Z DTEND:20230119T200000Z DTSTAMP:20260404T111000Z UID:OLS/109 DESCRIPTION:Title: The Solecki dichotomy and the Posner Robinson theorem\nby Patrick Lutz (UCLA) as part of Online logic seminar\n\n\nAbstract\nThe Solecki di chotomy in descriptive set theory\, roughly stated\, says that every Borel function on the real numbers is either a countable union of partial conti nuous functions or at least as complicated as the Turing jump. The Posner- Robinson theorem in computability theory\, again roughly stated\, says tha t every non-computable real looks like 0' relative to some oracle. Superfi cially\, these theorems look similar: both roughly say that some object is either simple or as complicated as the jump. However\, it is not immediat ely apparent whether this similarity is more than superficial. If nothing else\, the Solecki dichotomy is about third order objects—functions on t he real numbers—while the Posner-Robinson theorem is about second order objects—individual real numbers. We will show that there is a genuine ma thematical connection between the two theorems by showing that the Posner- Robinson theorem plus determinacy can be used to give a short proof of a s lightly weakened version of the Solecki dichotomy\, and vice-versa.\n LOCATION:https://stable.researchseminars.org/talk/OLS/109/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Hrušák (Universidad Nacional Autónoma de México) DTSTART:20230216T190000Z DTEND:20230216T200000Z DTSTAMP:20260404T111000Z UID:OLS/110 DESCRIPTION:Title: Model theory and topological groups\nby Michael Hrušák (Univers idad Nacional Autónoma de México) as part of Online logic seminar\n\n\nA bstract\nWe shall discuss some recent applications of model-theoretic meth ods to the study of topological groups. In particular\, we shall discuss s olutions to old problems of Comfort and van Douwen and the use of Fraissé theory to the study of groups of homeomorphisms.\n LOCATION:https://stable.researchseminars.org/talk/OLS/110/ END:VEVENT BEGIN:VEVENT SUMMARY:Maribel Fernandez (Kings College London) DTSTART:20230202T190000Z DTEND:20230202T200000Z DTSTAMP:20260404T111000Z UID:OLS/111 DESCRIPTION:Title: Nominal Techniques for the Specification of Languages with Binders\nby Maribel Fernandez (Kings College London) as part of Online logic sem inar\n\n\nAbstract\nThe nominal approach to the specification of languages with binding operators\, introduced by Gabbay and Pitts\, has its roots i n nominal set theory. Nominal logic is a theory of first-order logic that axiomatizes the notions of fresh name\, name swapping and abstraction from nominal sets\, making it an ideal tool for the specification of the seman tics of programming languages. In this talk\, we will start by recalling t he main concepts of nominal logic\, and then we will show how to apply the se ideas to specify calculi with binders. More precisely\, we will introdu ce nominal syntax (including the notions of fresh atoms and alpha-equivale nce)\, present matching and unification algorithms that take into account the alpha-equivalence relation\, define nominal rewriting (a generalisatio n of first-order rewriting that provides in-built support for alpha-equiva lence following the nominal approach) and give examples of application.\n LOCATION:https://stable.researchseminars.org/talk/OLS/111/ END:VEVENT BEGIN:VEVENT SUMMARY:Adele Padgett (McMaster University) DTSTART:20230126T190000Z DTEND:20230126T200000Z DTSTAMP:20260404T111000Z UID:OLS/112 DESCRIPTION:Title: Regular solutions of systems of transexponential polynomials\nby Adele Padgett (McMaster University) as part of Online logic seminar\n\n\nA bstract\nI will explain an open problem in the model theory of ordered fie lds and outline a possible strategy for resolving it. The problem is wheth er there are o-minimal fields that are “transexponential”\, i.e.\, whi ch define functions that eventually grow faster than any tower of exponent ials. In recent work\, I gave evidence indicating that a particular transe xponential expansion of the real field might be o-minimal. A possible next step would be to apply a criterion of Lion which grew out of Wilkie’s p roof that the real exponential field is o-minimal.\n LOCATION:https://stable.researchseminars.org/talk/OLS/112/ END:VEVENT BEGIN:VEVENT SUMMARY:Konstantin Slutsky (Iowa State University) DTSTART:20230302T190000Z DTEND:20230302T200000Z DTSTAMP:20260404T111000Z UID:OLS/114 DESCRIPTION:Title: Partial actions and orbit equivalence relations\nby Konstantin Sl utsky (Iowa State University) as part of Online logic seminar\n\n\nAbstrac t\nIn this talk\, we will discuss the framework of partial actions\nfor co nstructing orbit equivalent actions of Polish groups. While\nrelated ideas have been employed in ergodic theory and Borel\ndynamics for many years\, the particular viewpoint of partial\nactions simplifies construction of o rbit equivalent actions\nof distinct groups. \n\nAs an application\, we w ill present a Borel version of Katok's\nrepresentation theorem for multidi mensional Borel\nflows. One-dimensional flows are closely connected to act ions\nof $\\mathbb{Z}$ via the so-called "flow under a function"\nconstruc tion. This appealing geometric picture does not\ngeneralize to higher dim ensions. Within the ergodic theoretical\nframework\, Katok introduced the concept of a special flow as a\nway to connect multidimensional $\\mathbb {R}^d$ and $\\mathbb{Z}^d$\nactions. We will show that similar connection s continue to hold\nin Borel dynamics.\n\nAnother illustration of the part ial actions techniques that we\nintend to touch is the following result: a Borel equivalence\nrelation generated by a free R-flow can also be genera ted by a\nfree action of any non-discrete and non-compact Polish\ngroup. T his is in contrast with the situation for discrete\ngroups\, where amenabi lity distinguishes groups that can and\ncannot generate free finite measur e-preserving hyperfinite actions.\n LOCATION:https://stable.researchseminars.org/talk/OLS/114/ END:VEVENT BEGIN:VEVENT SUMMARY:Athar Abdul-Quader (Purchase College) DTSTART:20230323T180000Z DTEND:20230323T190000Z DTSTAMP:20260404T111000Z UID:OLS/115 DESCRIPTION:Title: Arithmetic Saturation and Pathological Satisfaction\nby Athar Abd ul-Quader (Purchase College) as part of Online logic seminar\n\n\nAbstract \nA classic result in models of arithmetic states that countable models of PA are recursively saturated if and only if they possess a "full satisfac tion class". A satisfaction class is a set of pairs (phi\, alpha)\, where phi is a code for a formula in the sense of the model\, and alpha is an as signment for that formula\, which extends the "standard" satisfaction rela tion\, and satisfies Tarksi's compositional rules for satisfaction. Recent ly\, there has been work on so-called pathological satisfaction classes: s atisfaction classes which exhibit certain pathologies\, like\, for example \, making sentences of the form "(0 = 1) or (0 = 1) or ... or (0 =1)" of n onstandard length true. We study these pathologies\, and find a surprising relationship between the question of determining which sets can be define d using certain pathologies\, and a stronger notion of saturation\, arithm etic saturation. This is joint work with Mateusz Łełyk\, based heavily o n unpublished work by Jim Schmerl.\n LOCATION:https://stable.researchseminars.org/talk/OLS/115/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Mourad (University of Connecticut) DTSTART:20230504T180000Z DTEND:20230504T190000Z DTSTAMP:20260404T111000Z UID:OLS/116 DESCRIPTION:Title: Computing Non-Repetitive Sequences Using the Lovász Local Lemma \nby Daniel Mourad (University of Connecticut) as part of Online logic sem inar\n\n\nAbstract\nWe discuss effective versions of classical results on the existence of non-repetitive sequences first proven using the Lovász L ocal Lemma\, a non-constructive existence result from the probabilistic me thod. We outline the path to these constructions. First\, a probabilistic resample algorithm converges to a witness to the Local Lemma in polynomial expected time. Then\, the bound on the expectation is used to build a det erministic algorithm with computable convergence time. However\, the resul ting effective computation has constraints that make it unsuitable for con structing non-repetitive sequences. We modify the resample algorithm and s how that these modifications allow us to relax these constraints\n LOCATION:https://stable.researchseminars.org/talk/OLS/116/ END:VEVENT BEGIN:VEVENT SUMMARY:Jenna Zomback (Williams College) DTSTART:20230316T180000Z DTEND:20230316T190000Z DTSTAMP:20260404T111000Z UID:OLS/117 DESCRIPTION:Title: Weak mixing for semigroup actions and applications to pointwise ergod ic theorems\nby Jenna Zomback (Williams College) as part of Online log ic seminar\n\n\nAbstract\nWe provide a sufficient condition for the natura l boundary action of free semigroups to be weak mixing. This result yields new pointwise ergodic theorems for free semigroup actions\, where the ave rages are taken along trees. This is joint work with Anush Tserunyan.\n LOCATION:https://stable.researchseminars.org/talk/OLS/117/ END:VEVENT BEGIN:VEVENT SUMMARY:Liling Ko (Ohio State University) DTSTART:20230209T190000Z DTEND:20230209T200000Z DTSTAMP:20260404T111000Z UID:OLS/118 DESCRIPTION:Title: Computable smallness is not intrinsic smallness\nby Liling Ko (Oh io State University) as part of Online logic seminar\n\n\nAbstract\nWe con struct a set $A$ that is computably small but not intrinsically small. To understand these terms\, we liken $A$ to a game show host playing against a class of computable contestants\, analogous to an infinite variant of th e Monty Hall problem. The host has infinitely many doors arranged in a lin e\, and each door hides either a goat or a car. A contestant selects infin itely many doors to open and wins if a non-zero density of the selected do ors hides a car. Contestants that are disorderly can select doors out of o rder\, opening door $i$ after door $j>i$. Are disorderly contestants more difficult to beat than orderly ones? This is known to be true if contestan ts are allowed to be adaptive\, where they may choose a different door dep ending on the outcomes of the previously opened ones [1] (via the theorem that MWC-stochasticity 0 does not imply Kolmogorov-Loveland-stochasticity 0). We give a constructive proof to show that the statement also holds in the non-adaptive setting\, shedding light on a disorderly structure that o utperforms orderly ones. This is joint work with Justin Miller.\n\n[1] Mer kle\, Wolfgang and Miller\, Joseph S and Nies\, Andre and Reimann\, Jan an d Stephan\, Frank. Kolmogorov--Loveland randomness and stochasticity. Anna ls of Pure and Applied Logic\, vol.138 (2006)\, no.1-3\, pp.183--210.\n LOCATION:https://stable.researchseminars.org/talk/OLS/118/ END:VEVENT BEGIN:VEVENT SUMMARY:Cian Dorr (New York University) DTSTART:20230427T180000Z DTEND:20230427T190000Z DTSTAMP:20260404T111000Z UID:OLS/119 DESCRIPTION:Title: Non-Extensional Higher Order Logic with Substitution\nby Cian Dor r (New York University) as part of Online logic seminar\n\n\nAbstract\nThe most widely studied systems of classical higher-order logic are ‘extens ional’ in the sense that they validate the schema ∀x₁…xₙ(Fx₁ …xₙ↔Gx₁…xₙ) → (F=G): intuitively\, this means that they coex tensive properties or relations are identical. Although this seems philos ophically suspect for obvious reasons\, the space of logics that keep the classical laws for propositional connectives and quantifiers while droppin g extensionality has been surprisingly little explored. This talk will ex plore a natural way of weakening extensionality by replacing it with the r ule ⊦Fx₁…xₙ↔Gx₁…xₙ / ⊦F=G\, or equivalently\, a rule tha t allows provably materially equivalent formulae to be intersubstituted an ywhere. I will give several very different axiomatizations of this system \, thereby cementing the case for its naturalness. After that I will disc uss a range of possible extensions of the system\, some of which restore c ertain arguably attractive consequences of extensionality\, and others of which take the view in a more “fine-grained” direction by systematical ly adding claims of non-identity which the basic system leaves unsettled. Finally\, I will describe a technique for constructing set-theoretic mode ls of the system\, which can be used to prove the consistency of many of t he aforementioned extensions. \n\nThe talk will be based on a forthcoming paper coauthored with Andrew Bacon\, available here: https://philarchive. org/rec/BACC-8.\n LOCATION:https://stable.researchseminars.org/talk/OLS/119/ END:VEVENT BEGIN:VEVENT SUMMARY:Sandra Müller (TU Wien) DTSTART:20230406T180000Z DTEND:20230406T190000Z DTSTAMP:20260404T111000Z UID:OLS/120 DESCRIPTION:Title: Canonical Models of Determinacy\nby Sandra Müller (TU Wien) as p art of Online logic seminar\n\n\nAbstract\nWoodin proved that every model of $\\mathsf{AD}^+$ (a natural strengthening of determinacy) is elementari ly equivalent to a derived model. In joint work with Sargsyan\, we establi shed a useful derived model representation for the Sealing model. In this talk\, I will outline this result (assuming no knowledge of inner model th eory) and describe its relevance for the inner model program.\n LOCATION:https://stable.researchseminars.org/talk/OLS/120/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexandra Soskova (Sofia University St. Kliment Ohridski) DTSTART:20230223T190000Z DTEND:20230223T200000Z DTSTAMP:20260404T111000Z UID:OLS/121 DESCRIPTION:Title: Cohesive Powers of Linear Orders\nby Alexandra Soskova (Sofia Uni versity St. Kliment Ohridski) as part of Online logic seminar\n\n\nAbstrac t\nCohesive powers of computable structures are effective analogs of ultra powers\, where cohesive sets play the role of ultrafilters. The aim is als o to compare and contrast properties of cohesive powers with those of clas sical\nultrapowers. Classically\, an ultrapower of a structure is elementa rily equivalent to the base structure by\nŁ\;oś\;'s theorem. Effec tively\, Ł\;oś\;'s theorem holds for cohesive powers of decidabl e structures. For cohesive powers of $n$-decidable structures\, Ł\;o& #347\;'s theorem need only\nhold up to $\\Delta_{n+3}$-expressible senten ces. In fact\, every $\\Sigma_{n+3}$ sentence true of an $n$-decidable\nst ructure is also true of all of its cohesive powers\, but this is optimal i n general. Classically\, ultrapowers of isomorphic structures over a fixed ultrafilter are isomorphic. Effectively\,\ncohesive powers of computably isomorphic computable structures over a fixed cohesive\nset are isomorphic . However\, it is possible for isomorphic (but not computably\nisomorphic) computable structures to have non-elementarily equivalent (hence non-isom orphic)\ncohesive powers. Classically\, the Keisler–Shelah theorem state s that two structures are elementarily equivalent if\nand only if there is an ultrafilter over which the corresponding\nultrapowers are isomorphic. Effectively\, an analogous result holds for decidable structures.\nIf the structures are computable that are not necessarily decidable\, then the\ne ffective version of the Keisler–Shelah theorem can fail in either direct ion. Classically\, for a countable language\, ultrapowers over countably i ncomplete ultrafilters are $\\aleph_1$-saturated. Effectively\, cohesive p owers of decidable structures are recursively saturated. Furthermore\, coh esive powers of n-decidable structures are $\\Sigma_n$-recursively saturat ed. Most interestingly\, if the cohesive set is assumed to be co-c.e.\, th en we obtain an additional level of saturation: cohesive powers of n-decid able structures over co-c.e.\ncohesive sets are $\\Sigma_{n+1}$-recursivel y saturated.\n\n\nWe investigate the cohesive powers of computable linear orders\, with special emphasis on computable copies of $\\omega$. If $\\m athcal{L}$ is a computable copy of $\\omega$ that is computably isomorphic to the standard presentation of $\\omega$\, then every cohesive power of $\\mathcal{L}$ has order-type $\\omega + \\zeta\\eta$. However\, there ar e computable copies of $\\omega$\, necessarily not computably isomorphic t o the standard presentation\, having cohesive powers not elementarily equi valent to $\\omega + \\zeta\\eta$. For example\, we show that there is a computable copy of $\\omega$ with a cohesive power of order-type $\\omega + \\eta$. Our most general result is that if $X \\subseteq \\mathbb N \\s etminus \\{0\\}$ is a Boolean combination of $\\Sigma_2$ sets\, thought o f as a set of finite order-types\, then there is a computable copy of $\\o mega$ with a cohesive power of order-type $\\omega + \\bm{\\sigma}(X \\cup \\{\\omega + \\zeta\\eta + \\omega^*\\})$\, where $\\bm{\\sigma}(X \\cup \\{\\omega + \\zeta\\eta + \\omega^*\\})$ denotes the shuffle of the order -types in $X$ and the order-type $\\omega + \\zeta\\eta + \\omega^*$. Fur thermore\, if $X$ is finite and non-empty\, then there is a computable cop y of $\\omega$ with a cohesive power of order-type $\\omega + \\bm{\\sigma }(X)$.\n\nThis is a joint work with Rumen Dimitrov\, Valentina Harizanov\, Andrey Morozov\, Paul Shafer and Stefan Vatev.\n\nIt was partially supp orted by Bulgarian National Science Fund KP-06-Austria-04/06.08.2019\,\nFN I-SU 80-10-134/20.05.2022.\n LOCATION:https://stable.researchseminars.org/talk/OLS/121/ END:VEVENT BEGIN:VEVENT SUMMARY:Una Stojnić (Princeton University) DTSTART:20230511T180000Z DTEND:20230511T190000Z DTSTAMP:20260404T111000Z UID:OLS/123 DESCRIPTION:by Una Stojnić (Princeton University) as part of Online logic seminar\n\n\nAbstract\nInferential Constraint and If φ ought φ Problem\ n\n \n\nThe standard semantics for modality\, together with the influentia l restrictor analysis of conditionals (Kratzer 1986\; 2012) validates cond itional constructions of the form ⌜φ$\\rightarrow$ □φ⌝. This is ba d news\; constructions like (1) aren’t intuitively trivially true:\n\n \ n\n1. If John's stealing\, he ought to be stealing.\n\n \n\nWhile this mig ht seem like a problem specifically for the restrictor analysis of conditi onals\, the issue is far more general. For any account must predict that m odals in the consequent sometimes receive obligatorily unrestricted interp retation\, as in (1)\, but sometimes appear restricted\, as in (2):\n\n \n \n2. If John's speeding\, he ought to pay the fine.\n\n \n\nAnd the proble m runs deeper\, for there are non-conditional variants of the problematic data. Thus\, the solution cannot lie in adopting a particular analysis of conditionals\, nor a specific account of the interaction between condition als and modals. Indeed\, with minimal assumptions\, the standard account o f modality will render a massive number of claims about what one ought to\ , must\, or may\, do trivially true. Worse\, the problem extends to a wide range of non-deontic modalities\, including metaphysical modality. But th e disaster has a remedy. I argue that the source of the problem lies in th e standard account’s failure to capture an inferential evidence constrai nt encoded in the meaning of a wide range of modal constructions. I offer a semantic account that captures this constraint\, and show it provides a general and independently motivated solution to the problem\, avoiding unw anted validities.\n LOCATION:https://stable.researchseminars.org/talk/OLS/123/ END:VEVENT BEGIN:VEVENT SUMMARY:Elliot Kaplan (McMaster University) DTSTART:20230330T180000Z DTEND:20230330T190000Z DTSTAMP:20260404T111000Z UID:OLS/124 DESCRIPTION:Title: Hilbert polynomials for finitary matroids\nby Elliot Kaplan (McMa ster University) as part of Online logic seminar\n\n\nAbstract\nEventual p olynomial growth is a common theme in combinatorics and commutative algebr a. The quintessential example of this phenomenon is the Hilbert polynomial \, which eventually coincides with the linear dimension of the graded piec es of a finitely generated module over a polynomial ring. A later result o f Kolchin shows that the transcendence degree of certain field extensions of a differential field is eventually polynomial. More recently\, Khovansk ii showed that for finite subsets A and B of a commutative semigroup\, the size of the sumset A+tB is eventually polynomial in t. I will present a c ommon generalization of these three results in terms of finitary matroids (also called pregeometries). I’ll discuss other instances of eventual po lynomial growth (like the Betti numbers of a simplicial complex) as well a s some applications to bounding model-theoretic ranks. This is joint work with Antongiulio Fornasiero.\n LOCATION:https://stable.researchseminars.org/talk/OLS/124/ END:VEVENT BEGIN:VEVENT SUMMARY:Michaël Cadilhac (DePaul University) DTSTART:20230914T180000Z DTEND:20230914T190000Z DTSTAMP:20260404T111000Z UID:OLS/126 DESCRIPTION:Title: Circuit Complexity as a Mathematician's Playground: Logic\, Algebra\, Combinatorics\nby Michaël Cadilhac (DePaul University) as part of On line logic seminar\n\n\nAbstract\nA (Boolean) circuit is a directed acycli c graph with AND\, OR\, and NOT nodes\, some input nodes\, and an output n ode\; they naturally compute Boolean functions. Circuit complexity is the study of how intricate or large a circuit needs to be in order to impleme nt a given Boolean function. If this description naturally hints to the u se of combinatorial tools\, circuit complexity also relies on finite model theory and deep algebraic concepts — specifically\, (profinite) semigro up theory. In this talk\, I will focus on a specific class of circuits\, depth-3 circuits\, and will explore a class of "simple" Boolean functions they express. In doing so\, I will go on a guided tour of the logical\, a lgebraic\, and combinatorial tools used in circuit complexity.\n\nBased on joint work with Corentin Barloy & Charles Paperman (U. Lille\, France) an d Thomas Zeume (Bochum U.\, Germany).\n LOCATION:https://stable.researchseminars.org/talk/OLS/126/ END:VEVENT BEGIN:VEVENT SUMMARY:(Cancelled) DTSTART:20231102T180000Z DTEND:20231102T190000Z DTSTAMP:20260404T111000Z UID:OLS/127 DESCRIPTION:Title: (Cancelled due to speaker illness\; will reschedule)\nby (Cancell ed) as part of Online logic seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/OLS/127/ END:VEVENT BEGIN:VEVENT SUMMARY:Kameryn Williams (Bard College at Simon's Rock) DTSTART:20231005T180000Z DTEND:20231005T190000Z DTSTAMP:20260404T111000Z UID:OLS/128 DESCRIPTION:Title: Interpretations and bi-interpretations in second-order arithmetic \nby Kameryn Williams (Bard College at Simon's Rock) as part of Online log ic seminar\n\n\nAbstract\nThe property of tightness\, introduced by Visser \, gives a notion of semantic completeness for a theory. Specifically\, a theory T is tight if any two distinct extensions of T cannot be bi-interpr etable. Important foundational theories like PA and ZF are tight. Conseque ntly interpretations of extensions of these theories must lose information . For example\, ZF + ¬AC can interpret ZFC by restricting to the construc tible universe while ZFC can interpret ZF + ¬AC via\, essentially\, forci ng. But these interpretations destroy information about the original unive rse\, and the tightness of ZF implies there are no alternative interpretat ions which avoid this problem.\n\nEnayat asked whether the full strength o f theories like ZF or full second-order arithmetic is necessary for the ti ghtness results and conjectured that this property can be used to give a c haracterization of these theories. Phrased in the contrapositive: must it be that any strict subtheory of these theories admits distinct\, bi-interp retable extensions? Alfredo Roque Freire and I investigated this question for subsystems of second-order arithmetic\, providing some evidence for En ayat’s conjecture. We showed that if you restrict the comprehension axio m to formulae of a bounded complexity then you can find two distinct yet b i-interpretable extensions of the theory. The main idea of the constructio n\, not uncommon for work in logic\, goes back to an old observation by Mo stowski. Namely\, while truth is not arithmetically definable\, it is defi nable over the arithmetical sets.\n LOCATION:https://stable.researchseminars.org/talk/OLS/128/ END:VEVENT BEGIN:VEVENT SUMMARY:Salma Kuhlmann (Universität Konstanz) DTSTART:20231026T180000Z DTEND:20231026T190000Z DTSTAMP:20260404T111000Z UID:OLS/129 DESCRIPTION:Title: The automorphism group of Hahn fields\nby Salma Kuhlmann (Univers ität Konstanz) as part of Online logic seminar\n\n\nAbstract\nSee abstrac t on seminar web page.\n LOCATION:https://stable.researchseminars.org/talk/OLS/129/ END:VEVENT BEGIN:VEVENT SUMMARY:Landon Elkind (Western Kentucky University) DTSTART:20231207T190000Z DTEND:20231207T200000Z DTSTAMP:20260404T111000Z UID:OLS/130 DESCRIPTION:Title: Principia Mathematica\, Negative Types\, and a theorem of infinity fo r Z-Principia Mathematica\nby Landon Elkind (Western Kentucky Universi ty) as part of Online logic seminar\n\n\nAbstract\nI here develop a new\, foundationless simple-type grammar to replace Principia Mathematica's well -founded simple-type grammar. Rewriting the axiom schemata of Principia in foundationless simple-types\, or Z-types\, gives us a new system\, ZPM. A dding to ZPM a plausible new axiom schema\, Z*107\, allows us prove Infini ty in every type. Z*107 is a plausible new axiom schema because\, as I wil l argue\, it is a logical truth of ZPM. Further\, using Z*107 to prove Inf inity is not circular: the new axiom alone does not secure a proof of Infi nity\, but crucially relies on heterogeneous relations. So using Z*107 to prove Infinity is not question-begging. In this talk I also relate this sy stem to earlier discussions of Wang's Negative Types (and its extension by Specker's TA).\n LOCATION:https://stable.researchseminars.org/talk/OLS/130/ END:VEVENT BEGIN:VEVENT SUMMARY:Isabella Scott (University of Chicago) DTSTART:20230824T180000Z DTEND:20230824T190000Z DTSTAMP:20260404T111000Z UID:OLS/131 DESCRIPTION:Title: Effective constructions of existentially closed groups\nby Isabel la Scott (University of Chicago) as part of Online logic seminar\n\n\nAbst ract\nExistentially closed groups were introduced in 1951 by group theoris ts\, in analogue with algebraically closed fields. Since then\, they have been further studied by Neumann\, Macintyre\, and Ziegler\, who elucidate d deep connections with model theory and computability theory. We review some of the literature on existentially closed groups and present new resu lts that further refine these connections. In particular we find a diverg ence between local and global complexity not visible from a purely algebra ic standpoint.\n LOCATION:https://stable.researchseminars.org/talk/OLS/131/ END:VEVENT BEGIN:VEVENT SUMMARY:Timothy Trujillo (Sam Houston State University) DTSTART:20230907T180000Z DTEND:20230907T190000Z DTSTAMP:20260404T111000Z UID:OLS/132 DESCRIPTION:Title: Nonstandard Methods in Topological Ramsey Theory: Revisiting the Nash -Williams Theorem\nby Timothy Trujillo (Sam Houston State University) as part of Online logic seminar\n\n\nAbstract\nIn this talk\, we explore t he application of nonstandard methods within the framework of topological Ramsey theory. Central to our discussion is a nonstandard proof of the Nas h-Williams theorem. We further investigate the potential of extending both the proof and the theorem's results to the abstract setting of topologica l Ramsey theory\, culminating in an examination of the abstract Nash-Willi ams theorem. Our aim is to offer an alternative perspective on well-establ ished results\, highlighting the intersections between nonstandard techniq ues and topological Ramsey theory.\n LOCATION:https://stable.researchseminars.org/talk/OLS/132/ END:VEVENT BEGIN:VEVENT SUMMARY:Darío García (Universidad de los Andes) DTSTART:20230921T180000Z DTEND:20230921T190000Z DTSTAMP:20260404T111000Z UID:OLS/133 DESCRIPTION:Title: Pseudofiniteness and measurability of the everywhere infinite forest< /a>\nby Darío García (Universidad de los Andes) as part of Online logic seminar\n\n\nAbstract\nA structure M is said to be pseudofinite if every f irst-order sentence that is true in M has a finite model\, or equivalently \, if M is elementarily equivalent to an ultraproduct of finite structures . For this kind of structures\, the fundamental theorem of ultraproducts ( Los' Theorem) provides a powerful connection between finite and infinite sets\, which can sometimes be used to prove qualitative properties of larg e finite structures using combinatorial methods applied to non-standard ca rdinalities of definable sets.\n\nThe concept of measurable structures was defined by Macpherson and Steinhorn in [2] as a method to study infinite structures with strong conditions of finiteness and definability for the s izes of definable sets. The most notable examples are the ultraproducts of asymptotic classes of finite structures (e.g.\, the class of finite field s or the class of finite cyclic groups). Measurable structures are supersi mple of finite SU-rank\, but recent generalizations of this concept are mo re flexible and allow the presence of structures whose SU-rank is possibly infinite.\n\nThe everywhere infinite forest is the theory of an acyclic g raph G such that every vertex has infinite degree. It is a well-known exam ple of an omega-stable theory of infinite rank. In this talk we will take this structure as a motivating example to introduce all the concepts menti oned above\, showing that it is pseudofinite and giving a precise descript ion of the sizes of their definable sets. In particular\, these results pr ovide a description of forking and U-rank for the infinite everywhere fore st in terms of certain pseudofinite dimensions\, and also show that it is a generalized measurable structure that can be presented as the ultraprodu ct of a multidimensional exact class of finite graphs. These results are j oint work with Melissa Robles\, and can be found in [1].\n\nReferences:\n\ n[1] Darío García and Melissa Robles. Pseudofiniteness and measurability of the everywhere infinite forest. Available at arXiv: https://arxiv.org/ pdf/2309.00991.pdf\n\n[2] Dugald Macpherson and Charles Steinhorn. One-dim ensional asymptotic classes of finite structures\, Transactions of the Ame rican Mathematical Society\, vol. 360 (2008)\n LOCATION:https://stable.researchseminars.org/talk/OLS/133/ END:VEVENT BEGIN:VEVENT SUMMARY:Dino Rossegger (Technische Universität Wien) DTSTART:20231019T180000Z DTEND:20231019T190000Z DTSTAMP:20260404T111000Z UID:OLS/134 DESCRIPTION:Title: Learning equivalence relations\nby Dino Rossegger (Technische Uni versität Wien) as part of Online logic seminar\n\n\nAbstract\nWhat does i t mean for an equivalence relation on a Polish space to be\nlearnable? Mot ivated by the recent work of Fokina\, Kötzing\, and San\nMauro\, who form ulated a framework to learn the isomorphism relation on\ncountable classes of structures\, we introduce frameworks that aim to\ngive a formal notion of learnability for equivalence relations on Polish\nspaces. Our main res ults characterize learnability in these frameworks\nvia the descriptive co mplexity of the equivalence relations\, and\, using\ntechniques from highe r recursion theory and effective descriptive set\ntheory\, we calculate th e complexity of the class of learnable\nequivalence relations. At last\, w e discuss the learnability of\nequivalence relations arising naturally in computability theory.\nThis is joint work with Ted Slaman and Tomasz Steif er.\n LOCATION:https://stable.researchseminars.org/talk/OLS/134/ END:VEVENT BEGIN:VEVENT SUMMARY:Assaf Shani (Concordia University\, Montreal) DTSTART:20231109T190000Z DTEND:20231109T200000Z DTSTAMP:20260404T111000Z UID:OLS/135 DESCRIPTION:Title: Generic analysis of Borel homomorphisms for the finite Friedman-Stanl ey jumps\nby Assaf Shani (Concordia University\, Montreal) as part of Online logic seminar\n\n\nAbstract\nThe talk will begin by discussing the basic definitions and general goals behind the theory of Borel equivalence relations. We will focus on the Friedman-Stanley jumps =+n\, for n=1\,2\, ... and n=ω. These Borel equivalence relations represent the notions of b eing classifiable using invariants which are countable sets of reals\, cou ntable sets of countable sets of reals\, and so on. We consider the proble m of constructing a Borel reduction from =+n to some other equivalence rel ation. For n=1 the situation is well understood and there are many such re sults. We present a technique for finding such a reduction when n>1\, base d on Baire-category analysis of all Borel homomorphisms from =+n.\n LOCATION:https://stable.researchseminars.org/talk/OLS/135/ END:VEVENT BEGIN:VEVENT SUMMARY:Teresa Kouri Kissel (Old Dominion University) DTSTART:20230928T180000Z DTEND:20230928T190000Z DTSTAMP:20260404T111000Z UID:OLS/136 DESCRIPTION:Title: Proof-Theoretic Pluralism and Harmony\nby Teresa Kouri Kissel (Ol d Dominion University) as part of Online logic seminar\n\n\nAbstract\nAbst ract: Ferrari and Orlandelli (2019) propose that an admissibility conditio n on a proof-theoretic logical pluralism be that the logics in question mu st be harmonious\, in the sense of Belnap (1962). This means that they mus t have connectives which are unique and conservative. This allows them to develop an innovative pluralism\, which shows variance on two levels. On o ne level\, we have a pluralism at the level of validity alone\, like that in Restall (2014). But\, thanks to the Ferrari and Orlandelli system\, whi ch was developed in response to some concerns of Kouri (2016)\, we can add a second level and admit some logics which do not share connective meanin gs\, and hence have different operational rules. This allows for us to hav e a pluralism at two levels: the level of validity and the level of connec tive meanings.\n\nHere\, I will show that we can extend the system one ste p further\, and induce a three-level logical pluralism. The first and seco nd levels remain as suggested by Ferrari and Orlandelli (2019)\, but we ca n allow for multiple notions of uniqueness in the definition of Belnap-har mony\, or multiple notions of harmony writ large. Either of these options generates a pluralism at the level of our admissibility conditions. This g enerates a pluralism at three levels: validity\, connective meanings\, and admissibility conditions. But it still preserves the spirit of the Ferrar i and Orlandelli (2019) solution: harmony remains as the admissibility con straint across the board\, and so the original worries of Kouri (2016) are still put to rest and the original Beall and Restall (2006) criteria for admissible logics are still met.\n LOCATION:https://stable.researchseminars.org/talk/OLS/136/ END:VEVENT BEGIN:VEVENT SUMMARY:Canceled DTSTART:20231116T190000Z DTEND:20231116T200000Z DTSTAMP:20260404T111000Z UID:OLS/137 DESCRIPTION:by Canceled as part of Online logic seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/OLS/137/ END:VEVENT BEGIN:VEVENT SUMMARY:Diana Carolina Montoya (Technische Universität Wien) DTSTART:20231130T190000Z DTEND:20231130T200000Z DTSTAMP:20260404T111000Z UID:OLS/138 DESCRIPTION:Title: Cardinal characteristics and singular cardinals\nby Diana Carolin a Montoya (Technische Universität Wien) as part of Online logic seminar\n \n\nAbstract\nThroughout the last few years\, many generalizations from cl assical cardinal characteristics of the Baire space have been studied. Spe cial interest has been given to the study of the combinatorics of the gene ralized Baire spaces $\\kappa^\\kappa$ when $\\kappa$ is an uncountable re gular cardinal (or even a large cardinal) but lately\, the generalization to singular cardinals has also been the focus of interest. In this talk\, I will present first the motivation within Set Theory to study these kinds of questions and afterward some results regarding a generalization to the context of singular cardinals of the concepts of maximal almost disjoint and maximal independence families and point out the differences concerning the regular case. Finally\, I will mention the open questions and possibl e future research paths in this area.\n LOCATION:https://stable.researchseminars.org/talk/OLS/138/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicholas Ramsey (University of Notre Dame) DTSTART:20231214T190000Z DTEND:20231214T200000Z DTSTAMP:20260404T111000Z UID:OLS/139 DESCRIPTION:Title: Model theory and the Lazard Correspondence\nby Nicholas Ramsey (U niversity of Notre Dame) as part of Online logic seminar\n\n\nAbstract\nTh e Lazard Correspondence is a characteristic $p$ analogue of the correspond ence between nilpotent Lie groups and Lie algebras\, associating to every nilpotent group of exponent $p$ and nilpotence class $c$ a Lie algebra ove r $F_p$ with the same nilpotence class (assuming $c < p$). We will describ e the role that this translation between nilpotent group theory and linear algebra has played in an emerging program to understand the first order p roperties of random nilpotent groups. In this talk\, we will focus on con nections to neostability theory\, highlighting the way that nilpotent grou ps furnish natural algebraic structures in surprising parts of the SOP$_n$ and $n$-dependence hierarchies. This is joint work with Christian d'Elb ée\, Isabel Müller\, and Daoud Siniora.\n LOCATION:https://stable.researchseminars.org/talk/OLS/139/ END:VEVENT BEGIN:VEVENT SUMMARY:Sam Sanders (Ruhr-Universität Bochum) DTSTART:20230831T180000Z DTEND:20230831T190000Z DTSTAMP:20260404T111000Z UID:OLS/140 DESCRIPTION:Title: The Biggest Five of Reverse Mathematics\nby Sam Sanders (Ruhr-Uni versität Bochum) as part of Online logic seminar\n\n\nAbstract\nI provide an overview of joint work with Dag Normann on the higher-order Reverse Ma thematics (RM for short) of the Big Five systems and the surprising limits of this enterprise ([3]).\n\nThe well-known Big Five phenomenon of RM is the observation that a large number of theorems from ordinary mathematics are either provable in the base theory or equivalent to one of only four s ystems\; these five systems together are called the ‘Big Five’ of RM. The aim of this paper is to greatly extend the Big Five phenomenon\, worki ng in Kohlenbach’s higher-order RM ([1]).\n\nIn particular\, we have est ablished numerous equivalences involving the second-order Big Five systems on one hand\, and well-known third-order theorems from analysis about (po ssibly) discontinuous functions on the other hand. We both study relativel y tame notions\, like cadlag or Baire 1\, and potentially wild ones\, like quasi-continuity. We also show that slight generalisations and variations (involving e.g. the notions Baire 2 and cliquishness) of the aforemention ed third-order theorems fall far outside of the Big Five. In particular\, these slight generalisations and variations imply the principle NIN from [ 2]\, i.e. there is no injection from [0\, 1] to N. We discuss a possible e xplanation for this phenomenon.\n\nREFERENCES.\n\n[1] Ulrich Kohlenbach\, Higher order reverse mathematics\, Reverse mathematics 2001\, Lect. Notes Log.\, vol. 21\, ASL\, 2005\, pp. 281–295.\n\n[2] Dag Normann and Sam Sa nders\, On the uncountability of R\, Journal of Symbolic Logic\, DOI: doi. org/ 10.1017/jsl.2022.27 (2022)\, pp. 43.\n\n[3] _________________________ \, The Biggest Five of Reverse Mathematics\, Submitted\, arxiv: https://ar xiv.org/abs/2212.00489 (2023)\, pp. 39.\n LOCATION:https://stable.researchseminars.org/talk/OLS/140/ END:VEVENT BEGIN:VEVENT SUMMARY:Noah Schweber (Proof School) DTSTART:20231012T180000Z DTEND:20231012T190000Z DTSTAMP:20260404T111000Z UID:OLS/141 DESCRIPTION:Title: Logic(s) in the computable context\nby Noah Schweber (Proof Schoo l) as part of Online logic seminar\n\n\nAbstract\nIn abstract model theory \, ``logic" is typically defined as something like ``An indexed family of isomorphism-respecting partitions of the class of all structures" - or mor e precisely\, an assignment of such partitions to signatures (usually we d emand some other conditions too). But we do not always think isomorphism-i nvariantly\; in particular\, when thinking about computable structures we typically ``carve up" the universe into equivalence classes with respect t o computable isomorphism.\n\nIn this talk I'll explore what there is to be said about ``abstract model theory in the computable universe." One logic we'll pay particular attention to is gotten by mixing classical computabl e infinitary logic with the notion of realizability coming from intuitioni stic arithmetic. This is work in progress\, so this talk will have lots of questions as well as results. No prior knowledge of intuitionistic logic will be assumed.\n LOCATION:https://stable.researchseminars.org/talk/OLS/141/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Icard (Stanford University) DTSTART:20240411T180000Z DTEND:20240411T190000Z DTSTAMP:20260404T111000Z UID:OLS/142 DESCRIPTION:Title: Causal Inference as a Logical Problem\nby Thomas Icard (Stanford University) as part of Online logic seminar\n\n\nAbstract\nThe aim of this talk will be to explain how problems of modern causal inference can be us efully and precisely understood as logical problems. Causal inquiry introd uces novel angles on traditional themes in logic (complexity\, definabilit y\, axiomatization\, etc.)\, and in the other direction\, mathematical and computational logic offers tools for clarifying questions in the theory o f causal inference.\n LOCATION:https://stable.researchseminars.org/talk/OLS/142/ END:VEVENT BEGIN:VEVENT SUMMARY:Russell Miller (City University of New York) DTSTART:20240118T190000Z DTEND:20240118T200000Z DTSTAMP:20260404T111000Z UID:OLS/143 DESCRIPTION:Title: Computability and absolute Galois groups\nby Russell Miller (City University of New York) as part of Online logic seminar\n\n\nAbstract\nTh e absolute Galois group $\\operatorname{Gal}(F)$\nof a field $F$ is the Galois group of its algebraic closure $\\overline{F}$\nrelative to $F $\, containing precisely those automorphisms of $\\overline{F}$\nthat fix $F$ itself pointwise. Even for a field as simple as the rational\nnumbers $\\mathbb{Q}$\, $\\operatorname{Gal}(\\mathbb Q)$ is a complicated\nobjec t. Indeed (perhaps counterintuitively)\, $\\operatorname{Gal}(\\mathbb Q) $\nis among the thorniest of all absolute Galois groups normally studied.\ n\nWhen $F$ is countable\, $\\operatorname{Gal}(F)$ usually has the cardin ality\nof the continuum. However\, it can be presented as the set of all paths\nthrough an $F$-computable finite-branching tree\, built by a proced ure\nuniform in $F$. We will first consider the basic properties of this tree\,\nwhich depend in some part on $F$. Then we will address questions\ nabout the subgroup consisting of the computable paths through\nthis tree\ , along with other subgroups\nsimilarly defined by Turing ideals. One nat urally asks to what\nextent these are elementary subgroups of $\\operatorn ame{Gal}(F)$\n(or at least elementarily equivalent to $\\operatorname{Gal} (F)$).\nThis question is connected to the computability of Skolem function s\nfor $\\operatorname{Gal}(F)$\, and also to the arithmetic complexity of \ndefinable subsets of $\\operatorname{Gal}(F)$.\n\nSome of the results th at will appear represent joint work with\nDebanjana Kundu.\n LOCATION:https://stable.researchseminars.org/talk/OLS/143/ END:VEVENT BEGIN:VEVENT SUMMARY:David Gonzalez (University of California Berkeley) DTSTART:20240201T190000Z DTEND:20240201T200000Z DTSTAMP:20260404T111000Z UID:OLS/144 DESCRIPTION:Title: Generically computable linear orderings\nby David Gonzalez (Unive rsity of California Berkeley) as part of Online logic seminar\n\n\nAbstrac t\nW. Calvert\, D\, Cenzer and V. Harizanov introduced notions of generic computability for structures that are stratified by the computable ordinal s. In a recent collaboration with these authors we examined these notions in the context of linear orderings. Our main results contrast one another. We show that every linear ordering has a 1-generically computable copy. O n the other hand\, we have that the set of linear orderings with a n-gener ically computable copy for n>1 is as complicated as possible: Sigma 1 1-co mplete.\n\nThis talk will put these results in context and describe the ne w\, more structural approach we took to this problem. In particular\, I wi ll describe these results through the lens of a surprising connection with Ramsey-like properties.\n LOCATION:https://stable.researchseminars.org/talk/OLS/144/ END:VEVENT BEGIN:VEVENT SUMMARY:David Meretzky (University of Notre Dame) DTSTART:20240509T180000Z DTEND:20240509T190000Z DTSTAMP:20260404T111000Z UID:OLS/145 DESCRIPTION:Title: Differential Field Arithmetic\nby David Meretzky (University of N otre Dame) as part of Online logic seminar\n\n\nAbstract\nI will discuss s ome of my upcoming thesis work under the supervision of Anand Pillay. Some of this work is also joint with Omar León Sánchez. Motivated by existen ce questions in differential Galois theory\, I will discuss our recent eff orts to generalize a theorem of Serre from the algebraic to the differenti al algebraic setting. Serre's theorem states: A field F is bounded (has fi nitely many extensions of each finite degree) if and only if the first Gal ois cohomology set with coefficients in any linear algebraic group defined over F is trivial. This talk will emphasize our development of basic com putational tools for definable Galois cohomology\, a model theoretic gener alization of (differential) algebraic Galois cohomology. All of the releva nt notions will be introduced\, including some background on differential Galois theory.\n LOCATION:https://stable.researchseminars.org/talk/OLS/145/ END:VEVENT BEGIN:VEVENT SUMMARY:Ellen Hammatt (Victoria University of Wellington) DTSTART:20240215T190000Z DTEND:20240215T200000Z DTSTAMP:20260404T111000Z UID:OLS/146 DESCRIPTION:Title: Punctual Structures\nby Ellen Hammatt (Victoria University of Wel lington) as part of Online logic seminar\n\n\nAbstract\nIn this talk we in vestigate what happens when we take concepts from computable structure the ory and forbid the use of unbounded search. In other words\, we discuss th e primitive recursive content of structure theory. This central definition is that of punctual structures\, introduced by Kalimullin\, Melnikov and Ng in 2017. We investigate various concepts from computable structure theo ry in the primitive recursive case. A common theme is that new techniques are required in the primitive recursive case. We also discuss a degree str ucture within punctual presentations which is induced by primitive recursi ve isomorphisms. This degree structure is a new concept that does not aris e in computable structure theory.\n LOCATION:https://stable.researchseminars.org/talk/OLS/146/ END:VEVENT BEGIN:VEVENT SUMMARY:Jamshid Derakhshan (Oxford University) DTSTART:20240208T190000Z DTEND:20240208T200000Z DTSTAMP:20260404T111000Z UID:OLS/147 DESCRIPTION:Title: Decidability of the class of all the rings $Z/mZ$: A problem of Ax\nby Jamshid Derakhshan (Oxford University) as part of Online logic semin ar\n\n\nAbstract\nIn his celebrated 1968 paper on the elementary theory of finite fields James Ax asked if the theory of the class of all the rings $Z/mZ$\, for all $m>1$\, is decidable. In that paper\, Ax proved that the existential theory of this class is decidable using his result that the th eory of all the rings $Z/p^nZ$ (with $p$ and $n$ varying) is decidable. Th is used Chebotarev’s density theorem and Ax's pioneering work and axioma tization of the theory of pseudo-finite fields. In that paper Ax proved th at the theory of the class of all finite fields is decidable.\n\nIn this t alk I will present joint work with Angus Macintyre giving a solution to Ax ’s problem. Our solution uses some previous work of ours on the model th eory of the ring of adeles. These are locally compact rings associated to number fields and have been of fundamental importance in number theory eve r since they were introduced by Chevalley\, Weil\, Artin. Interestingly Ax ’s problem can be reduced to the decidability of the ring of adeles of t he rational numbers. So while the theory of pseudo-finite fields governs t he theory of all finite fields as shown by Ax\, the theory of all $Z/mZ$ i s governed by the theory of the rational adele ring.\n\n(This work is publ ished in Forum of Mathematics\, Sigma\, 24 July 2023.)\n LOCATION:https://stable.researchseminars.org/talk/OLS/147/ END:VEVENT BEGIN:VEVENT SUMMARY:Vincent Guingona (Towson University) DTSTART:20240314T180000Z DTEND:20240314T190000Z DTSTAMP:20260404T111000Z UID:OLS/148 DESCRIPTION:Title: Configurations and Products of Classes\nby Vincent Guingona (Tows on University) as part of Online logic seminar\n\n\nAbstract\nIn this talk \, I will discuss the notion of a "configuration" where the index is a cla ss of structures and the target is an arbitrary theory. This gives us a m ethod of classifying theories based on their ability to encode positive co mbinatorial configurations\, similar to the non-collapse of generalized in discernibles. We will examine desirable properties of the index class\, s uch as indivisibility\, and how these properties are closed under differen t product operations.\n\nSome of this work is joint with M. Parnes and L. Scow.\n LOCATION:https://stable.researchseminars.org/talk/OLS/148/ END:VEVENT BEGIN:VEVENT SUMMARY:Miriam Parnes (Towson University) DTSTART:20240328T180000Z DTEND:20240328T190000Z DTSTAMP:20260404T111000Z UID:OLS/149 DESCRIPTION:by Miriam Parnes (Towson University) as part of Online logic s eminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/OLS/149/ END:VEVENT BEGIN:VEVENT SUMMARY:Jessica Schirle (University of California Irvine) DTSTART:20240307T190000Z DTEND:20240307T200000Z DTSTAMP:20260404T111000Z UID:OLS/150 DESCRIPTION:Title: Gaming Models by Buildings\nby Jessica Schirle (University of Cal ifornia Irvine) as part of Online logic seminar\n\n\nAbstract\nIn continuo us model theory\, as in the classical setting\, if one has an appropriatel y sized unstable structure A in a countable language\, then depending on t he truth of CH\, there's either a unique or 2c many nonisomorph ic ultrapowers of A as we vary the choice of ultrafilter on ω. A similar statement may be made in regards to ultraproducts and sequences of structu res that exhibit an order property.\n\nIn a partial answer to a question o f Gromov\, Kramer et al. showed that there is a finitely presented group s uch that\, depending on the truth of CH\, this group has either a unique o r 2c many asymptotic cones up to homeomorphism. Asymptotic cone s of metric spaces are realized as particular metric ultraproducts. The Kr amer et al. paper does not formalize the obvious model theoretic connectio n\, but does comment on the combinatorial-geometric structure of the asymp totic cones\, which was known to Thornton (and independently to Kramer and Tent) and is a certain kind of building.\n\nIn this talk\, we'll give a b rief overview of work done by Luther to formalize this model theoretic con nection. Special attention will be given to Ehrenfeucht-Fraïssé games an d how the building structure can give us additional tools to develop a pos sible winning strategy for Player II in games between (what are potentiall y) non-homeomorphic asymptotic cones of certain symmetric spaces.\n LOCATION:https://stable.researchseminars.org/talk/OLS/150/ END:VEVENT BEGIN:VEVENT SUMMARY:Leonardo Coregliano (University of Chicago) DTSTART:20240926T180000Z DTEND:20240926T190000Z DTSTAMP:20260404T111000Z UID:OLS/152 DESCRIPTION:Title: Exchangeable random structures and quasirandomness\nby Leonardo C oregliano (University of Chicago) as part of Online logic seminar\n\n\nAbs tract\nA random structure on a vertex set $V$ (in a fixed finite relationa l language) is exchangeable if\nits distribution is invariant under permut ations of $V$. The Aldous--Hoover Theorem says all such\ndistributions are generated from a collection of i.i.d. variables on $[0\,1]$\, one for eac h subset\nof $V$\, using a simple rule that was later called "Euclidean st ructure" by combinatorialists. As the\nname suggests\, an Euclidean struct ure resembles a relational structure over $[0\,1]$\, except for the\nprese nce of "higher-order variables".\n\nOne of the original questions of Hoove r was to determine which such distributions admit simpler\ndescriptions\, that do not depend on certain variables. Very little progress was obtained in this\nproblem until it got revisited under the light of the theories o f limits of combinatorial objects\nand quasirandomness. It turns out that asking for a representation of an exchangeable hypergraph in\nwhich the Eu clidean structure is a usual (measurable) relational structure over $[0\,1 ]$ (i.e.\, which\ndoes not need any higher-order variables) is equivalent to asking for "tamer" Szemeré\;di regularity\nlemmas and was solved using the theory of hypergraphons.\n\nThe dual problem of determining when there is a representation that does not need any low-order\nvariable is m ore closely related to quasirandomness\, which informally is the property of "lack of\ncorrelation with simple structures".\n\nIn this talk\, I will introduce exchangeability and quasirandomness theory and talk about recen t\nprogress on the aforementioned dual problem. I will assume familiarity with basic logic/model\ntheory\, but no prior knowledge in extremal combin atorics\, limit theory or quasirandomness will be\nnecessary.\n\nThis talk is based on joint works with Alexander Razborov and Henry Towsner.\n LOCATION:https://stable.researchseminars.org/talk/OLS/152/ END:VEVENT BEGIN:VEVENT SUMMARY:Brian Zilli (Iowa State University) DTSTART:20240425T180000Z DTEND:20240425T190000Z DTSTAMP:20260404T111000Z UID:OLS/153 DESCRIPTION:Title: On the spectra of computable bounded analytic functions\nby Brian Zilli (Iowa State University) as part of Online logic seminar\n\n\nAbstra ct\nMcNicholl\, in collaboration with Matheson and later individually\, sh owed that a Blaschke product is computable if and only if it has a computa ble zero sequence with computable Blaschke constant. The spectrum of a Bla schke product is the set of accumulation points of its zeros. We use Mathe son and McNicholl's results to consider the arithmetical complexity of suc h spectra for computable Blaschke products. Namely\, we present results sh owing that all such spectra are $\\Sigma^0_3$--closed\, that there exists a $\\Sigma^0_3$--complete spectrum\, that every $\\Pi^0_2$--closed subset of the unit circle is a spectrum\, and that there exists a $\\Sigma^0_2$-- closed set which is not.\n\n\nWe then turn our attention to uniform Frostm an Blaschke products\, shown by Frostman to be those with nontangential li mits of modulus one everywhere (as opposed to generic Blaschke products wh ich\, as inner functions\, are only guaranteed to have radial limits of mo dulus one almost everywhere). Matheson showed that the spectra of such fun ctions are precisely the closed\, nonempty\, and nowhere dense subsets of the unit circle. We discuss an effectivization of one direction of his res ult\, showing that every computably closed\, nonempty\, and nowhere dense subset of the circle is the spectrum of a computable uniform Frostman Blas chke product.\n\nJoint work with Timothy McNicholl\n LOCATION:https://stable.researchseminars.org/talk/OLS/153/ END:VEVENT BEGIN:VEVENT SUMMARY:Marcelo E. Coniglio (University of Campinas (UNICAMP)) DTSTART:20240502T180000Z DTEND:20240502T190000Z DTSTAMP:20260404T111000Z UID:OLS/154 DESCRIPTION:Title: Decision procedures for Intuitionistic logic and for modal logic S4 b y 3-valued non-deterministic matrices\nby Marcelo E. Coniglio (Univers ity of Campinas (UNICAMP)) as part of Online logic seminar\n\n\nAbstract\n In 1932 Gödel proved that it is impossible to characterize\nintuitionisti c propositional logic (IPL) by a single finite logical\nmatrix\, that is\, by finite-valued truth-tables. By adapting Gödel's\nproof\, J. Dugundji proved in 1940 that no modal system between Lewis'\nS1 and S5 can be chara cterized by a single finite logical matrix. That\nis\, the usual modal log ics are also not characterizable by finite-valued\ntruth-tables. As a way to overcome Dugundji’s result\, J. Kearns\nintroduced in 1981 a 4-valued non-deterministic matrix (Nmatrix\, for\nshort) for modal logics KT\, S4\ , and S5 in which just a subset of the\nvaluations are allowed (that valua tions are called "level\nvaluations"). He proved that this restricted Nmat rix (RNmatrix\, for\nshort) constitutes a sound and complete semantics for these modal\nlogics. However\, Kearns’s level valuations fail to provid e an\neffective decision procedure for these modal logics. Recently\, L.\n Grätz refined Kearn’s original RNmatrix to obtain a decidable 3-valued\ nRNmatrix for modal logics KT and S4\, by using an appropriate\nnotion of partial valuation for level semantics.\nThanks to the conservative transla tion from IPL into S4 introduced by\nGödel in 1933\n(which is also comput able)\, by composing both algorithms a decision\nprocedure for IPL is obta ined.\n\nIn this talk the Grätz algorithm will be described\, as well as a new algorithm\nfor deciding validity in IPL obtained by considering anot her translation\nderived from Gödel's one. It allows defining the compose d algorithm\nfor IPL above mentioned\, but in a direct way\, hence the sou ndness and\ncompleteness of the method is proved independently of Gödel a nd Grätz results.\nIn this way\, an original 3-valued RNmatrix for IPL is defined\, with a\nvery natural\ninterpretation\, as well as an easy algor ithm which allows to remove\,\nfrom the truth\ntables generated by the 3-v alued Nmatrix\, those rows which are not\nsound. This decision\nprocedure\ , as well as Grätz's one\, were implemented in Coq. This is a\njoint work with Renato\nLeme and Bruno Lopes.\n LOCATION:https://stable.researchseminars.org/talk/OLS/154/ END:VEVENT BEGIN:VEVENT SUMMARY:Java Darleen Villano (University of Connecticut) DTSTART:20241024T180000Z DTEND:20241024T190000Z DTSTAMP:20260404T111000Z UID:OLS/155 DESCRIPTION:Title: Computable categoricity relative to a degree\nby Java Darleen Vil lano (University of Connecticut) as part of Online logic seminar\n\n\nAbst ract\nA computable structure $\\mathcal{A}$ is said to be computably categ orical relative to a degree $\\mathbf{d}$ if for all $\\mathbf{d}$-computa ble copies $\\mathcal{B}$ of $\\mathcal{A}$\, there exists a $\\mathbf{d}$ -computable isomorphism between $\\mathcal{A}$ and $\\mathcal{B}$. In 2021 result by Downey\, Harrison-Trainor\, and Melnikov\, it was shown that th ere exists a computable graph $\\mathcal{G}$ such that for an infinite inc reasing sequence of c.e.\\ degrees $\\mathbf{x}_0 <_T \\mathbf{y}_0 <_T \\ mathbf{x}_1 <_T \\mathbf{y}_1\\dots$\, $\\mathcal{G}$ was computably categ orical relative to each $\\mathbf{x}_i$ but not computably categorical rel ative to each $\\mathbf{y}_i$.  That is\, the behavior of categoricity re lative to a degree is not monotonic under $\\mathbf{0}'$. In this talk\, w e will sketch how to extend this result for partial orders of c.e.\\ degre es\, and discuss some future directions of this project.\n LOCATION:https://stable.researchseminars.org/talk/OLS/155/ END:VEVENT BEGIN:VEVENT SUMMARY:Jinhe Ye (University of Oxford) DTSTART:20241010T180000Z DTEND:20241010T190000Z DTSTAMP:20260404T111000Z UID:OLS/156 DESCRIPTION:Title: Hyperbolicity and model complete fields\nby Jinhe Ye (University of Oxford) as part of Online logic seminar\n\n\nAbstract\nGiven $C$ a (qua si-projective) curve over $\\mathbb{Q}$ with genus at least 2 and $C(\\mat hbb{Q})$ is empty\, the class of fields $K$ of characteristic 0 such that $C(K)=\\emptyset$ has a model companion CXF. Models of CXF have an interes ting combination of properties and provide examples to answer various ques tions around model theory of fields\, field arithmetic\, and decidability. \n\nIt turns out the existence of model companion is related to several no tions of hyperbolicity in algebraic geometry. In particular\, with the ass umptions of different notions of hyperbolicity on V\, our results admit ge neralisation to varieties V of arbitrary dimension. This talk is based on joint work with Will Johnson and joint work with Michal Szachniewicz.\n LOCATION:https://stable.researchseminars.org/talk/OLS/156/ END:VEVENT BEGIN:VEVENT SUMMARY:Leo Jimenez (Ohio State University) DTSTART:20240912T180000Z DTEND:20240912T190000Z DTSTAMP:20260404T111000Z UID:OLS/157 DESCRIPTION:Title: Internality of autonomous systems of differential equations\nby L eo Jimenez (Ohio State University) as part of Online logic seminar\n\n\nAb stract\nWhen solving a differential equation\, one sometimes finds that so lutions can be expressed using a finite number of fixed\, particular solut ions\, and some complex numbers. As an example\, the set of solutions of a linear differential equation is a finite-dimensional complex vector space . A model-theoretic incarnation of this phenomenon is internality to the c onstants in a differentially closed field of characteristic zero. In this talk\, I will define what this means\, and discuss some recent progress\, joint with Christine Eagles\, on finding concrete methods to determine whe ther or not the solution set of a differential equation is internal. A cor ollary of our method also gives a criteria for solutions to be Liouvillian : I will show a concrete application to Lotka-Volterra systems.\n LOCATION:https://stable.researchseminars.org/talk/OLS/157/ END:VEVENT BEGIN:VEVENT SUMMARY:Julia Knight (Notre Dame) DTSTART:20241121T190000Z DTEND:20241121T200000Z DTSTAMP:20260404T111000Z UID:OLS/158 DESCRIPTION:Title: Complexity of well-ordered sets in an ordered Abelian group\nby J ulia Knight (Notre Dame) as part of Online logic seminar\n\n\nAbstract\nWe consider the following three basic problems\, plus some variants.\n\n1. H ow hard is it to say of a countable well-ordering that it has type at leas t $\\alpha$?\n\n2. How hard is it to say of well-ordered sets $A\,B$ in an ordered Abelian group $G$ that the set $A+B = \\{a+b:a\\in A\\ \\&\\ b\\i n B\\}$ has type at least $\\alpha$?\n\n3. How hard is it to say of a well -ordered set $A$ of non-negative elements in an ordered Abelian group $G$ that the set $[A]$ consisting of finite sums of elements of $A$ has type a t least $\\alpha$? \n\n\nEach problem asks the complexity of membership a smaller class $K$\, assuming membership in a larger class $K^*$. We want to measure complexity in the Borel and effective Borel hierarchies. Howev er\, the classes $K^*$ and $K$ are not Borel. Calvert's notions of comple xity and completeness within allow us to measure complexity in the way we want\, setting upper bounds\, and showing that the bounds are sharp . \n\nAuthors: Chris Hall\, Julia Knight\, and Karen Lange\n LOCATION:https://stable.researchseminars.org/talk/OLS/158/ END:VEVENT BEGIN:VEVENT SUMMARY:Charles McCoy (University of Portland) DTSTART:20241107T190000Z DTEND:20241107T200000Z DTSTAMP:20260404T111000Z UID:OLS/159 DESCRIPTION:Title: Computable $\\Pi^0_2$ Scott Sentences\nby Charles McCoy (Universi ty of Portland) as part of Online logic seminar\n\n\nAbstract\nAbstract av ailable at http://lagrange.math.siu.edu/Calvert/OnlineSeminar/McCoy2024abs tract.pdf\n LOCATION:https://stable.researchseminars.org/talk/OLS/159/ END:VEVENT BEGIN:VEVENT SUMMARY:Dicle Mutlu (McMaster University) DTSTART:20241114T190000Z DTEND:20241114T200000Z DTSTAMP:20260404T111000Z UID:OLS/160 DESCRIPTION:Title: Definable groups in henselian valued fields\nby Dicle Mutlu (McMa ster University) as part of Online logic seminar\n\n\nAbstract\nA valued f ield is henselian if every simple root of a polynomial in its residue fiel d lifts uniquely to a root in the field itself. The Ax-Kochen-Ershov Princ iple states that henselian valued fields are—in the model-theoretic sens e—determined by their value groups and residue fields\, which are much s impler mathematical structures. This naturally leads to the question: Can every definable group in a henselian valued field be decomposed into compo nents that are controlled by its value group and residue field? Hrushovski and Rideau-Kikuchi have answered this question positively for abelian gro ups in algebraically closed valued fields. In this talk\, we will discuss our approach and results extending their work to the broader henselian set ting. This is joint work with Paul Z. Wang.\n LOCATION:https://stable.researchseminars.org/talk/OLS/160/ END:VEVENT BEGIN:VEVENT SUMMARY:Sunil Karn (Southern Illinois University) DTSTART:20241205T190000Z DTEND:20241205T200000Z DTSTAMP:20260404T111000Z UID:OLS/161 DESCRIPTION:Title: Behaviorally Correct Language Identification.\nby Sunil Karn (Sou thern Illinois University) as part of Online logic seminar\n\n\nAbstract\n The concept of Behaviorally Correct (BC) language identification\, is a pa radigm in inductive inference that allows learners to approximate target l anguages while tolerating a bounded density of errors. Beginning with foun dational definitions\, such as those of inductive inference machines (IIMs ) and BC identification\, we extend these notions to approximate identific ation using error densities and asymptotic uniform densities. Our results demonstrate the structured inclusion relations between various identificat ion classes. Specifically\, we prove that for any r\, r1​∈ [0\,1] with r1​> r\, TxtBCr ​⊂ TxtBCr1\, and similarly UBCr​ ⊂ UBCr1​​ and UTxtBCr ​⊂ UTxtBCr1\, indicating that relaxation of error bounds y ields strictly larger identification classes.\n\nFurthermore\, leveraging the Operator Recursion Theorem\, we construct examples demonstrating the n on-equivalence of adjacent identification classes\, highlighting the role of partial recursive functions in these separations. These results emphasi ze the versatility of BC identification frameworks in accommodating error densities while maintaining robust theoretical guarantees. Finally\, we in troduce uniform approximate BC identification and establish its utility in addressing local inconsistencies within language approximation\, culminat ing in refined criteria that bridge global and local error bounds.\n LOCATION:https://stable.researchseminars.org/talk/OLS/161/ END:VEVENT BEGIN:VEVENT SUMMARY:Don Stull (University of Chicago) DTSTART:20241003T180000Z DTEND:20241003T190000Z DTSTAMP:20260404T111000Z UID:OLS/162 DESCRIPTION:Title: Recent progress on distance sets in the plane\nby Don Stull (Univ ersity of Chicago) as part of Online logic seminar\n\n\nAbstract\nRecent w ork has shown that techniques from algorithmic randomness can be used to u nderstand questions in classical geometric measure theory. One of the cent ral problems in geometric measure theory is Falconer's distance set conjec ture. Give a set E in the plane\, and a point x\, the pinned distance set of E with respect to x is the set of distances between x and the points in E. In this talk\, I will discuss recent work which uses algorithmic rando mness to improve the best known lower bounds for both the Hausdorff and pa cking dimensions of pinned distance sets. This is joint work with Jacob Fi edler.\n LOCATION:https://stable.researchseminars.org/talk/OLS/162/ END:VEVENT BEGIN:VEVENT SUMMARY:Janani Lakshmanan (University of Hawaii) DTSTART:20241031T180000Z DTEND:20241031T190000Z DTSTAMP:20260404T111000Z UID:OLS/163 DESCRIPTION:Title: New Measures of Automatic Complexity Arising from Quantum Logic\n by Janani Lakshmanan (University of Hawaii) as part of Online logic semina r\n\n\nAbstract\nThe automatic complexity of finite words was introduced b y Shallit and Wang (2001). It measures the complexity of a word $x$ as the minimum number of states of a finite automaton that uniquely accepts $x$. Here\, an automaton $M$ uniquely accepts a word $x$ if $x$ is the only wo rd of length $|x|$ accepted by $M$. Via the digraph representation of auto mata we can view the computation of this number of states as a problem of extremal graph theory. A quantum version of automatic complexity was first studied by Kjos-Hanssen (2017). In this talk\, we explore several new mea sures of automatic complexity motivated by the geometric subspace structur e of the automata and the associated quantum logic. In keeping with the Ha llowe'en spirit\, We consider some generalizations of quantum finite autom ata with the application of an immortality constraint\, considering a fami ly of automata without dead states.\n LOCATION:https://stable.researchseminars.org/talk/OLS/163/ END:VEVENT BEGIN:VEVENT SUMMARY:Sam Sanders (RUB Bochum) DTSTART:20241017T180000Z DTEND:20241017T190000Z DTSTAMP:20260404T111000Z UID:OLS/164 DESCRIPTION:Title: Some results in reverse mathematics inspired by proof mining\nby Sam Sanders (RUB Bochum) as part of Online logic seminar\n\n\nAbstract\nTh e study of (compact) metric spaces in second-order Reverse Mathematics (RM hereafter) is fundamentally based on separability conditions\, while the latter are generally avoided in proof mining to enable the extraction of g ood computational data. Inspired by this observation\, we study basic prop erties of ‘unrepresented’ compact metric spaces in Kohlenbach’s high er-order RM\, i.e. we do not assume separability conditions. Our results a re four-fold as follows\, each building on the next.\n\nMost definitions o f compactness yield third-order theorems not provable from second-order co mprehension axioms. Only one very specific choice of compactness definitio ns yields equivalences involving the so-called Big Five of second-order RM .\n\nMany basic properties of compact metric spaces inhabit the range of h yperarithmetical analysis. Until recently\, few natural examples of the la tter were known.\n\nSome basic properties of compact metric spaces\, like the intermediate value theorem\, are equivalent to countable choice as stu died in higher-order RM\, namely QF-AC0\,1.\n\nSome basic properties of co mpact metric spaces\, like a continuous function has a supremum and a coun table set has measure zero\, imply strong axioms including Feferman’s pr ojection principle\, full second-order arithmetic\, and Kleene’s quantif ier (∃3).\n\nIn conclusion\, the removal of separability conditions from compact metric spaces results in rather interesting phenomena.\n LOCATION:https://stable.researchseminars.org/talk/OLS/164/ END:VEVENT BEGIN:VEVENT SUMMARY:Victoria Gitman (CUNY Graduate Center) DTSTART:20250206T190000Z DTEND:20250206T200000Z DTSTAMP:20260404T111000Z UID:OLS/165 DESCRIPTION:Title: Parameter-free schemes in second-order arithmetic\nby Victoria Gi tman (CUNY Graduate Center) as part of Online logic seminar\n\n\nAbstract\ nSecond-order arithmetic has two types of objects: numbers and set of numb ers\, which we think of as the reals. Which sets (reals) have to exist in a model of second-order arithmetic is determined by the various set-existe nce axioms. These usually come in the form of schemes\, of which the most common are the comprehension scheme\, the choice scheme\, and the collecti on scheme. The \\emph{comprehension scheme} $\\Sigma^1_n$-${\\rm CA}$ asse rts for a $\\Sigma^1_n$-formula $\\varphi(n\,A)$\, with a set parameter $A $\, that the collection it determines is a set. The \\emph{choice scheme} $\\Sigma^1_n$-${\\rm AC}$ asserts for a $\\Sigma^1_n$-formula $\\varphi(n\ ,X\,A)$ that if for every number $n$ there is a set $X$ such that $\\varph i(n\,X\,A)$ holds\, then there is a single set $Y$ such that its slice $Y_ n$ is a witness for $n$. The \\emph{collection scheme} $\\Sigma^1_n$-${\\r m Coll}$ asserts more generally that among the slices of $Y$\, there is a witness for every $n$. The full comprehension scheme for all second-order assertions is denoted by ${\\rm Z}_2$\, the full choice scheme by ${\\rm AC}$\, and the full collection scheme by ${\\rm Coll}$. Although the theor ies ${\\rm Z}_2$+${\\rm AC}$ and ${\\rm Z}_2$ are equiconsistent\, Feferma n and L\\' evy showed that ${\\rm AC}$ is independent of ${\\rm Z}_2$. It is also not difficult to see that ${\\rm Coll}$ implies ${\\rm Z}_2$ over $\\Sigma^1_0$-${\\rm CA}$\, and hence that ${\\rm Coll}$ implies ${\\rm AC }$ over $\\Sigma^1_0$-${\\rm CA}$.\n\nIn this talk\, I will explore how si gnificant the inclusion of set parameters is in the second-order set-exist ence schemes. Let ${\\rm Z}_2^{-p}$\, ${\\rm AC}^{-p}$\, and ${\\rm Coll}^ {-p}$ denote the respective parameter-free schemes. H. Friedman showed tha t the theories ${\\rm Z}_2$ and ${\\rm Z}_2^{-p}$ are equiconsistent and r ecently Kanovei and Lyubetsky showed that the theory ${\\rm Z}_2^{-p}$ can have extremely badly behaved models in which the sets aren't even closed under complement. They also constructed a more ``nice" model of ${\\rm Z}_ 2^{-p}$ in which $\\Sigma^1_2$-${\\rm CA}$ holds\, but $\\Sigma^1_4$-${\\r m CA}$ fails. They asked whether one can construct a model of ${\\rm Z}_2^ {-p}$ in which $\\Sigma^1_2$-${\\rm CA}$ holds\, but there is an optimal f ailure of $\\Sigma^1_3$-${\\rm CA}$. I will answer their question by const ructing such a model. I will also construct a model of ${\\rm Z}_2^{-p}+{\ \rm Coll}^{-p}$ in which $\\Sigma^1_2$-${\\rm CA}$ holds\, but ${\\rm AC}^ {-p}$ fails\, thus showing that ${\\rm Coll}^{-p}$ does not imply ${\\rm A C}^{-p}$ even over $\\Sigma^1_2$-${\\rm CA}$.\n LOCATION:https://stable.researchseminars.org/talk/OLS/165/ END:VEVENT BEGIN:VEVENT SUMMARY:Nikolaos Galatos (University of Denver) DTSTART:20250403T180000Z DTEND:20250403T190000Z DTSTAMP:20260404T111000Z UID:OLS/166 DESCRIPTION:Title: Tight complexity bounds for substructural logics\nby Nikolaos Gal atos (University of Denver) as part of Online logic seminar\n\n\nAbstract\ nSubstructural logics constitute generalizations of classical and intuitio nistic logic that allow for resource sensitive reasoning\; they connect to philosophy\, computer science\, engineering\, mathematical linguistics an d theoretical physics. Their algebraic semantics\, residuated lattices\, h ave their independent history and relate to ring theory\, lattice-ordered groups and Tarski’s relation algebras\, among other algebraic structures . \n\n We discuss the complexity of provability and of deduciblity of vari ous substructural logics\, ranging from low complexity classes to undecida bility. Of particular interest are certain knotted extensions which have ( non-elementary) complexity in the Ackermann level of the fast-growing hier archy. We obtain lower complexity bounds by encoding suitable and-branchin g counter machines into the corresponding algebraic semantics\, using the method of residuated frames. For the upper bounds\, we undertake a proof-t heoretic investigation of auxiliary analytic calculi and employ methods fr om the theory of well-ordered sets to obtain length theorems. Together\, t hese yield tight complexity bounds for the logics under investigation. Our results cover both sequent and hypersequent calculi.\n LOCATION:https://stable.researchseminars.org/talk/OLS/166/ END:VEVENT BEGIN:VEVENT SUMMARY:Ulla Karhumäki (University of Helsinki) DTSTART:20250220T190000Z DTEND:20250220T200000Z DTSTAMP:20260404T111000Z UID:OLS/167 DESCRIPTION:Title: Pseudofinite primitive permutation groups of finite SU-rank\nby U lla Karhumäki (University of Helsinki) as part of Online logic seminar\n\ n\nAbstract\nA (definably) primitive permutation group (G\,X) is a group G together with a transitive faithful and definable action on X such that t here are no proper nontrivial (definable) G-invariant equivalence relation s on X. Definably primitive permutation groups of finite Morley rank are w ell-studied: in particular\, it is shown by Macpherson and Pillay that suc h a group with infinite point stabilisers is actually primitive and by Bor ovik and Cherlin that\, given such a group (G\,X)\, the Morley rank of G c an be bounded in terms of the Morley rank of X. We show similar results fo r a pseudofinite definably primitive permutation group (G\,X) of finite SU -rank: we first show that (G\,X) is primitive if and only if the point sta bilisers are infinite. This then allows us to apply a classification resul t by Liebeck\, Macpherson and Tent on (G\,X) so that we may bound the SU-r ank of G in terms of the SU-rank of X. This is joint work in with Nick Ram sey.\n LOCATION:https://stable.researchseminars.org/talk/OLS/167/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew DeLapo (University of Connecticut) DTSTART:20250213T190000Z DTEND:20250213T200000Z DTSTAMP:20260404T111000Z UID:OLS/168 DESCRIPTION:Title: Index Sets and Computable Categoricity of CSC Spaces\nby Andrew D eLapo (University of Connecticut) as part of Online logic seminar\n\n\nAbs tract\nGiven a topology on the natural numbers\, how complicated is it to describe? To answer this question with tools from computability theory\, w e will restrict to the context of countable second-countable (CSC) topolog ical spaces. One approach is to assign an index to each computable CSC spa ce and determine the arithmetic complexity of the set of CSC spaces with s ome property. Another approach comes from computable structure theory\; fo r example\, given two computable copies of a CSC space\, does there exist a computable homeomorphism between them? In this talk\, we will explore th ese approaches and apply them in three running examples: the indiscrete\, discrete\, and initial segment topologies.\n LOCATION:https://stable.researchseminars.org/talk/OLS/168/ END:VEVENT BEGIN:VEVENT SUMMARY:Theodore Slaman (University of California Berkeley) DTSTART:20250123T190000Z DTEND:20250123T200000Z DTSTAMP:20260404T111000Z UID:OLS/169 DESCRIPTION:Title: Extending Borel's Conjecture from Measure to Dimension\nby Theodo re Slaman (University of California Berkeley) as part of Online logic semi nar\n\n\nAbstract\nWe discuss the general formulation of Hausdorff dimensi on in terms of gauge measures from the meta-mathematical perspective. The re is a natural generalization to the context of dimension of Borel's conj ecture that only countable sets have strong measure zero. We show that th is generalization is consistent with ZFC. \n\nWe propose the question "Fo r which ideals I of gauge measures H does there exist a set such that H(A) >0 exactly when H is an element of I?" We settle a question of C. Rogers (1962) to show that the answer to this question depends on the descriptive complexity of A. In particular\, the answer for closed sets is different from that for (even low-level) Borel sets.\n LOCATION:https://stable.researchseminars.org/talk/OLS/169/ END:VEVENT BEGIN:VEVENT SUMMARY:Pablo Barcelo (Pontificia Universidad Cató\;lica de Chile) DTSTART:20250320T180000Z DTEND:20250320T190000Z DTSTAMP:20260404T111000Z UID:OLS/170 DESCRIPTION:Title: The Role of Logic in Advancing Machine Learning: Three Case Studies\nby Pablo Barcelo (Pontificia Universidad Cató\;lica de Chile) as part of Online logic seminar\n\n\nAbstract\nIn this paper\, I present thr ee case studies from my collaborative research that highlight the essentia l role of logic in enhancing our understanding of modern machine learning architectures. The first two examples focus on the expressive capabilities of two prominent architectures: Transformers\, which have revolutionized NLP applications\, and Graph Neural Networks\, a leading approach for clas sifying graph-structured data. We employ temporal logic techniques to anal yze the properties that Transformers can recognize\, and modal logics to e xamine the properties discernible by Graph Neural Networks. The third exam ple addresses the pursuit of explainable AI\, demonstrating how first-orde r logic can be used to design languages that declare\, evaluate\, and comp ute explanations for decisions made by machine learning models.\n LOCATION:https://stable.researchseminars.org/talk/OLS/170/ END:VEVENT BEGIN:VEVENT SUMMARY:Pedro Zambrano (Universidad Nacional de Colombia at Bogotá\; ) DTSTART:20250327T180000Z DTEND:20250327T190000Z DTSTAMP:20260404T111000Z UID:OLS/171 DESCRIPTION:Title: Quantale-Valued Model Theory and Set Theory\nby Pedro Zambrano (U niversidad Nacional de Colombia at Bogotá\;) as part of Online logic seminar\n\n\nAbstract\nIn this talk\, we will discuss a generalization of Continuous Logic\, where the distances take values in suitable quantales. By assuming suitable conditions (e.g.\, being\nco-divisibility -substract ability-\, being a co-Girard and a V-domain)\, we provide a proof of a ver sion of the Tarski-Vaught test and Łoś Theorem in our setting. Iovino pr oved that there is no logic properly extending Continuous Logic satisfying both Countable Tarski-Vaught chain Theorem and Compactness Theorem\, obta ining in this way a new approach of Continuous Logic. This part is a joint work with David Reyes. Also\, we will talk about a generalization of Fitt ing’s work on Intuitionistic Kripke models of Set Theory using Ono’s a nd Komori’s Residuated Kripke models. Based on these models\, we provide a generalization of the von Neumann hierarchy in the context of Modal Res iduated Logic (close to quantales) and prove a translation of formulas bet ween it and a suited Heyting valued model. This part is a joint work with Jose R. Moncayo.\n LOCATION:https://stable.researchseminars.org/talk/OLS/171/ END:VEVENT BEGIN:VEVENT SUMMARY:Antonio Nakid Cordero (University of Wisconsin) DTSTART:20250410T180000Z DTEND:20250410T190000Z DTSTAMP:20260404T111000Z UID:OLS/172 DESCRIPTION:Title: Martin's conjecture in the enumeration degrees\nby Antonio Nakid Cordero (University of Wisconsin) as part of Online logic seminar\n\n\nAbs tract\nMartin's conjecture is a long open problem that seeks to prove the empirical observation that "naturally occurring" Turing degrees are well-o rdered. The conjecture posits that the only natural constructions of incom putable degrees arise from iterations of the Turing jump. Even though the full conjecture remains open\, several significant partial results have be en obtained both in the Turing degrees and by translating the conjecture t o other degree structures.\n\n The study of the enumeration degrees has g ained relevance in recent years for their applications to effective mathem atics and for their structural connections to the Turing degrees. In this setting\, Martin's conjecture is relevant due to the existence of a defin able copy of the Turing degrees inside the enumeration degrees and two nat ural operations that extend the Turing jump: the enumeration jump and the skip. However\, the unique features of the enumeration degrees pose challe nges to even formulating an analogue to Martin's conjecture.\n\n I will p resent a surprising positive result based on Bard's local approach to the uniform Martin's conjecture. From this\, we can prove part 1 of Martin's c onjecture for uniformly Turing-to-enumeration invariant functions. Additio nally\, I discuss several counterexamples\, including an invariant functio n in the enumeration degrees that fails to be uniformly invariant.\n LOCATION:https://stable.researchseminars.org/talk/OLS/172/ END:VEVENT BEGIN:VEVENT SUMMARY:Juan Pablo de Rasis (Ohio State University) DTSTART:20250306T190000Z DTEND:20250306T200000Z DTSTAMP:20260404T111000Z UID:OLS/173 DESCRIPTION:Title: Definability problems regarding Campana points and Darmon points\ nby Juan Pablo de Rasis (Ohio State University) as part of Online logic se minar\n\n\nAbstract\nCampana points and Darmon points arise in algebraic g eometry to generalize m-full integers and perfect m-th powers\, respective ly\, to more arbitrary varieties. In this talk we will study the problem o f defining these objects over number fields using first-order language\, a nd we will conclude by building on a result by Fritz\, Pasten\, and Pheida s which shows that the diophantineness of Campana points on complex ration al functions in one variable is incompatible with Kollar's conjecture\, an argument that can be easily adapted for Darmon points as well. This will motivate further research on the analogous definability of these sets over C(z).\n LOCATION:https://stable.researchseminars.org/talk/OLS/173/ END:VEVENT BEGIN:VEVENT SUMMARY:Isis Gallardo (University of Denver) DTSTART:20250313T180000Z DTEND:20250313T190000Z DTSTAMP:20260404T111000Z UID:OLS/174 DESCRIPTION:Title: Decidability and generation of the variety of distributive $\\ell$-pr egroups.\nby Isis Gallardo (University of Denver) as part of Online lo gic seminar\n\n\nAbstract\nLattice-ordered pregroups ($\\ell$-pregroups) r epresent a natural generalization of lattice ordered groups ($\\ell$-group s). It is well-established that every $\\ell$-group can be embedded into a symmetric one\, as demonstrated by Cayley-Holland’s embedding theorem. Analogously\, a Cayley-Holland’s embedding theorem exists for distributi ve $\\ell$-pregroups\, asserting that any distributive $\\ell$-pregroup ca n be embedded into a functional one. In this work\, we enhance this result by establishing that any distributive $\\ell$-pregroup can be embedded in to a functional one over a chain that is locally isomorphic to $\\mathbb{Z }$. Utilizing this\, we demonstrate that the variety of distributive $\\el l$-pregroups is generated by the (single) functional algebra over the inte gers. We will later use this to prove the decidability of the variety.\n LOCATION:https://stable.researchseminars.org/talk/OLS/174/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicola Gambino (University of Manchester) DTSTART:20250227T190000Z DTEND:20250227T200000Z DTSTAMP:20260404T111000Z UID:OLS/175 DESCRIPTION:Title: Monoidal bicategories\, differential linear logic\, and analytic func tors\nby Nicola Gambino (University of Manchester) as part of Online l ogic seminar\n\n\nAbstract\nDifferential linear logic\, introduced by Ehrh ard and Regnier\, is an extension of linear logic with a differentiation o peration. It is interesting both from a syntactic point of view\, since it leads to a new technique to study λ-calculus (via Taylor series expansio n of λ-terms)\, and a semantical one\, as its models are categories in wh ich morphisms can be differentiated. The talk will present a new model of differential linear logic\, based on Joyal’s analytic functors\, which a re a functorial counterpart of exponential power series. This model can be understood as a ‘categorified’ version of the relational model of Lin ear Logic.\n LOCATION:https://stable.researchseminars.org/talk/OLS/175/ END:VEVENT BEGIN:VEVENT SUMMARY:Uri Andrews (University of Wisconsin) DTSTART:20250417T180000Z DTEND:20250417T190000Z DTSTAMP:20260404T111000Z UID:OLS/176 DESCRIPTION:Title: Group word problems revisited\nby Uri Andrews (University of Wisc onsin) as part of Online logic seminar\n\n\nAbstract\nPre-dating computabi lity theory\, Max Dehn proposed to find algorithms to answer\, for a given group presentation\, word problem of the group: whether two given words in the generators are equal in the group. Novikov and Boone showed in the 50s that some simply presented groups can have undecidable word problem. I n fact\, every r.e. degree contains the word problem of a finitely present ed group. From the perspective of the Turing degrees\, this gives a comple te answer to the question of the complexity of word problems of groups. Th e answer is: Every possible complexity.\n\nI will present a different pers pective on studying word problem complexity: We study the complexity of wo rd problems as equivalence relations under computable reducibility. That i s\, we say that an equivalence relation R reduces to an equivalence relati on E if there is a computable function f so that xRy if and only if f(x) E f(y). In this structure\, we find a more subtle picture\, beginning with the fact that not every degree is the degree of a the word problem of a gr oup. Some surprising phenomena appear. Work joint with Turbo Ho and Luca S an Mauro.\n LOCATION:https://stable.researchseminars.org/talk/OLS/176/ END:VEVENT BEGIN:VEVENT SUMMARY:Heidi Benham (University of Connecticut) DTSTART:20250424T180000Z DTEND:20250424T190000Z DTSTAMP:20260404T111000Z UID:OLS/177 DESCRIPTION:Title: Problem Reducibility of Weakened Ginsburg—Sands Theorem\nby Hei di Benham (University of Connecticut) as part of Online logic seminar\n\n\ nAbstract\nA recent paper by Benham\, DeLapo\, Dzhafarov\, Solomon\, and V illano entitled “Ginsburg—Sands theorem and computability theory” an alyzes computability theoretical and reverse mathematical strength of a to pological theorem by Ginsburg and Sands\, along with several weakened vers ions. The original theorem states that every infinite topological space ha s an infinite subspace homeomorphic to one of the following on the natural numbers: indiscrete\, initial segment\, final segment\, discrete\, or cof inite. In this original paper\, it is claimed that the theorem is a conseq uence of Ramsey’s Theorem\, and though it has been shown by Benham\, DeL apo\, Dzhafarov\, Solomon\, and Villano that the full theorem is equivalen t over RCA_0 to ACA_0\, there is a weakened version that is equivalent ove r RCA_0 to CAC (Chain-antichain Principle)\, a consequence of Ramsey’s T heorem. One interesting feature of the proof of this equivalence is that\, not only an application CAC\, but also an application of ADS (Ascending/d escending Sequence Principle)\, which is a consequence of CAC\, is used. T his inspires the question of whether this weakened version of the Ginsburg —Sands Theorem and CAC\, when viewed as problems\, are Weihrauch equival ent.\n\nI will present some new progress that has been made on this questi on. This progress involves developing several new combinatorial problems r elated to CAC and ADS\, one of which is Weihrauch equivalent to the weaken ed version of the Ginsburg—Sands Theorem\, and showing a variety of Weih rauch and computable reducibilities between them.\n LOCATION:https://stable.researchseminars.org/talk/OLS/177/ END:VEVENT BEGIN:VEVENT SUMMARY:Laura Gamboa Guzmá\;n (Iowa State University) DTSTART:20250501T180000Z DTEND:20250501T190000Z DTSTAMP:20260404T111000Z UID:OLS/178 DESCRIPTION:Title: Formalizing Time: Temporal Logics and the Challenge of Visualizing ML TL\nby Laura Gamboa Guzmá\;n (Iowa State University) as part of Online logic seminar\n\n\nAbstract\nTemporal logics are a family of modal logics that reason about timelines. They are usually obtained by expanding classical propositional logic with modal operators that can qualify the v alue of a proposition over time\, such as “p will always be true” or “q is true until p becomes true.” However\, different concepts of time are often captured by significant logical systems\, as these tend to enco de the various characteristics that define them\, such as continuous vs. d iscrete time and linear vs. branching time. The use and development of the se logics have been increasing significantly over the last 50 years\, as r esearchers and engineers in fields related to computer science have been u sing them to verify safety-critical systems in a formal and precise manner . \n\nIn this talk\, I will introduce some of the better-known temporal lo gics that aim to formalize different concepts of time and briefly explain the different properties that make them good candidates for use in differe nt computer-based environments. After that\, I will focus on a logic I hav e been working on during my PhD known as Mission-time (Linear) Temporal Lo gic (MLTL)\, which is a logic that reasons about finite and discrete timel ines (called traces) where finite intervals bound the temporal operators. Although MLTL is only as expressive as classical propositional logic\, it has been capturing the attention of multiple research groups in recent yea rs\, and its succinctness has shown to become a challenge for engineers ea sily when trying to validate the formulas they believe are capturing the d esired behaviors. For that\, at the Laboratory for Temporal Logic at ISU\, we have been developing algorithms that allow us to take an MLTL formula and produce a visual representation for the traces that satisfy the formul a.\n LOCATION:https://stable.researchseminars.org/talk/OLS/178/ END:VEVENT BEGIN:VEVENT SUMMARY:Krzysztof Mierzewski (Carnegie Mellon University) DTSTART:20250508T180000Z DTEND:20250508T190000Z DTSTAMP:20260404T111000Z UID:OLS/179 DESCRIPTION:Title: The logics of kernels and closures\nby Krzysztof Mierzewski (Carn egie Mellon University) as part of Online logic seminar\n\n\nAbstract\nEac h subset D of a complete Boolean algebra generates both a closure operator and a kernel operator on the algebra\, respectively mapping each element to its lower approximation (the join of all D-elements below it) and its u pper approximation (the meet of all D-elements above it). I will discuss t he bimodal logics of such approximation operators on Boolean algebras. By varying the constraints imposed on the generating set D\, we obtain a natu ral family of modal logics. The resulting algebraic approximation semantic s offers a new perspective on several common modal systems: I will show ho w well-known modal logics can be recovered as logics of approximation for particular choices of constraints on the generating set\, and one can trac e the emergence of various modal laws to simple structural features of the generating set. The logic of approximation operators generated by arbitra ry subsets D is the subnormal logic EMNT4+EMNT4. I will give a simple crit erion that characterizes the corresponding class of algebras: that is\, al gebras with abstract closure and kernel operators that are representable a s approximation operators. The complete logic of approximation operators g enerated by a sublattice is the fusion S4+S4: the completeness result reli es on a correspondence between sublattice-generated approximation operator s and pairwise zero-dimensional bitopological spaces. When D is a complete sublattice\, we obtain exactly the temporal logic S4t. When D is a subalg ebra\, the two modalities collapse into one as they become each other’s duals\, and we obtain monomodal S5 (for complete subalgebras) and S4 (for subalgebras in general).\n LOCATION:https://stable.researchseminars.org/talk/OLS/179/ END:VEVENT BEGIN:VEVENT SUMMARY:Emma Gruner (Penn State University) DTSTART:20250904T180000Z DTEND:20250904T190000Z DTSTAMP:20260404T111000Z UID:OLS/180 DESCRIPTION:Title: A Baire Category Approach to Besicovitch's Theorem\nby Emma Grune r (Penn State University) as part of Online logic seminar\n\n\nAbstract\nO ne of the fundamental results from geometric measure theory is Besicovitch 's theorem from 1952\, which states that any closed subset of Euclidean sp ace having infinite Hausdorff measure contains a compact subset with posit ive finite Hausdorff measure. However\, the computatibility theoretic and reverse mathematical complexity of this result have not been extensively s tudied. In this talk\, we will introduce a variant of the Baire Category T heorem\, and show how we can reframe Besicovitch's original proof through that lens. This approach not only confirms that the theorem is provable in $\\text{ACA}_0$\, but demonstrates how a witnessing subset can be compute d from just one jump of the original set.\n LOCATION:https://stable.researchseminars.org/talk/OLS/180/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabriel Poesia (Harvard University) DTSTART:20251106T190000Z DTEND:20251106T200000Z DTSTAMP:20260404T111000Z UID:OLS/181 DESCRIPTION:Title: Learning formal mathematical abstractions\nby Gabriel Poesia (Har vard University) as part of Online logic seminar\n\n\nAbstract\nMathematic al abstractions are devices that enable general representations of many co ncrete mathematical objects at once: they include definitions\, lemmas\, p roof strategies and algorithms. Typically\, computer agents applied in for mal mathematics are given a set of human-created abstractions (e.g.\, defi nitions\, tactics\, lemmas in Lean's mathematical library) and receive tas ks that involve using and combining those (e.g.\, proving a given theorem) . This talk will instead focus on our work on automatically learning the a bstractions themselves. We'll first describe our initial work on this line on learning problem-solving tactics for Khan Academy algebra problems in a simple dependently-typed theorem proving environment. Then\, we will use these principles to learn tactics in the Rocq (formerly Coq) theorem prov er from existing corpora of human proofs. In both cases\, tactic learning is operationalized by a symbolic compression procedure\, a principle that has been fruitful in learning abstractions in the field of program synthes is. I'll end by briefly describing ongoing work on a compression-based lib rary learning method for terms in Lean's type theory\, and highlight sever al applications of this tool. In particular\, compressing sets of theorem statements yields new mathematical definitions that help compactly rewrite the statements\, whereas compressing proof terms gives rise to lemmas tha t shorten existing proofs.\n LOCATION:https://stable.researchseminars.org/talk/OLS/181/ END:VEVENT BEGIN:VEVENT SUMMARY:Annalisa Conversano (Massey University) DTSTART:20250828T180000Z DTEND:20250828T190000Z DTSTAMP:20260404T111000Z UID:OLS/182 DESCRIPTION:Title: Groups and rings in o-minimal structures\nby Annalisa Conversano (Massey University) as part of Online logic seminar\n\n\nAbstract\nAfter a short introduction to o-minimality\, I will try to explain connections an d interactions between groups and rings that are definable in arbitrary o- minimal structures and familiar objects over the real field: Lie groups an d associative algebras. All definitions will be recalled\, and many exampl es will be used to illustrate the general theory.\n LOCATION:https://stable.researchseminars.org/talk/OLS/182/ END:VEVENT BEGIN:VEVENT SUMMARY:John Goodrick (Universidad de los Andes) DTSTART:20250918T180000Z DTEND:20250918T190000Z DTSTAMP:20260404T111000Z UID:OLS/183 DESCRIPTION:Title: Expansions of ordered Abelian groups by unary predicates\nby John Goodrick (Universidad de los Andes) as part of Online logic seminar\n\n\n Abstract\nI will talk about some recent results on model-theoretic tamenes s properties of expansions of ordered Abelian groups by unary predicates. In particular\, I will discuss properties such as (strongly) NIP\, having finite dp-rank\, and dp-minimality and how these relate to topological and arithmetic properties of sets definable in the structure. Furthermore I w ill present some ongoing work on quantifier elimination for expansions of regular ordered abelian groups by a predicate for a dense subgroup.\n LOCATION:https://stable.researchseminars.org/talk/OLS/183/ END:VEVENT BEGIN:VEVENT SUMMARY:Jin Wei (University of Pennsylvania) DTSTART:20251009T180000Z DTEND:20251009T190000Z DTSTAMP:20260404T111000Z UID:OLS/184 DESCRIPTION:Title: A Gentzen-Style Proof System for First-Order Łukasiewicz Logic and I ts Completeness\nby Jin Wei (University of Pennsylvania) as part of On line logic seminar\n\n\nAbstract\nContinuous model theory for metric struc tures is grounded in first-order Łukasiewicz logic and thus inherits an H ilbert-style axiomatization. However\, the syntactic study with this proof system encounters difficulties\, mainly the failure of the deduction theo rem due to issues with contraction. Gentzen-style proof systems for Łukas iewicz Logic have been developed to address these challenges\, with hypers equent calculi for propositional and first-order Łukasiewicz Logic introd uced by Metcalfe\, Olivetti\, and Gabbay (2005) and Baaz and Metcalfe (201 0). In this talk\, I will give a brief introduction to their work and pres ent my own result establishing the first-order completeness. I will also d iscuss potential directions of research\, including syntax cut elimination and the development of a constructive fragment of Łukasiewicz Logic\, wi th potential applications to continuous logic.\n LOCATION:https://stable.researchseminars.org/talk/OLS/184/ END:VEVENT BEGIN:VEVENT SUMMARY:Cé\;cilia Pradic (Swansea University) DTSTART:20251016T180000Z DTEND:20251016T190000Z DTSTAMP:20260404T111000Z UID:OLS/185 DESCRIPTION:Title: How unconstructive is the Cantor-Bernstein theorem?\nby Cé\ ;cilia Pradic (Swansea University) as part of Online logic seminar\n\n\nAb stract\nBased on joint work with Chad Brown [1] and [2].\nThe Cantor-Berns tein theorem states that sizes of sets can be compared meaningfully using injections: if A injects into B and vice-versa\, A and B are in bijection. This is typically proven via an explicit construction that does not invol ve choice\, but the proof cannot be constructive. For instance\, [0\,1] an d (0\,1) can be embedded into one another but are not homeomorphic\, meani ng that Cantor-Bernstein is violated in a number of models of intuitionist ic set theory. Faced with this state of affairs\, we can still ask: how ba d it is?\nFirst\, we are going to see how Cantor-Bernstein implies full ex cluded middle. We will then turn our attention to the Myhill isomorphism t heorem\, a constructive version of Cantor-Bernstein that states that\, for any two subsets A\, B ⊆ ℕ that are inter-reducible via injections\, t here is a bijection ℕ → ℕ that preserves them. The theorem remains t rue classically if ℕ is replaced by an arbitrary set X\, but this is not the case constructively. Bauer asked if there is a nice class of sets X f or which it does hold constructively. After checking there is no hope for this class of sets to be closed under basic operations like disjoint union s\, we will see that a version of this generalized Myhill isomorphism theo rem holds for the conatural numbers ℕ∞ by adapting the usual back-and- forth construction and assuming Markov's principle. However\, this does no t extend much: this fails for 2× ℕ∞\, ℕ + ℕ∞ as well as Cantor space. We are going to see why those failures are of different flavours\, and sketch how to make this more precise by using oracle modalities.\n\n1. Pradic\, C. and Brown\, C. E. 2022. Cantor-Bernstein implies Excluded Mid dle. arXiv preprint arXiv:1904.09193.\n\n2. Pradic\, C. 2025. The Myhill i somorphism theorem does not generalize much. arXiv preprint arXiv:2507.050 28.\n LOCATION:https://stable.researchseminars.org/talk/OLS/185/ END:VEVENT BEGIN:VEVENT SUMMARY:Anton Freund (Universitä\;t Wü\;rzburg) DTSTART:20250925T180000Z DTEND:20250925T190000Z DTSTAMP:20260404T111000Z UID:OLS/186 DESCRIPTION:Title: Well-ordering principles and the reverse mathematics zoo\nby Anto n Freund (Universitä\;t Wü\;rzburg) as part of Online logic semina r\n\n\nAbstract\nOver the moderately strong base theory ACA$_0$ from rever se mathematics\, any $\\Pi^1_2$-statement corresponds to a transformations of well-orders (i.e.\, to a dilator). We will show that\, in contrast\, t here is a dichotomy over the weaker base theory RCA$_0$. Here\, transforma tions of well-orders are either weak or have a certain minimal strength. I t follows that $\\Pi^1_2$-statements in a certain gap cannot correspond to a transformation of well-orders. Ramsey's theorem for pairs is a particul arly prominent $\\Pi^1_2$-statement in this gap. The talk is based on https://doi.org/10.1142/S0 219061325500102. It is directed at a general logical audience.\n LOCATION:https://stable.researchseminars.org/talk/OLS/186/ END:VEVENT BEGIN:VEVENT SUMMARY:Jason Block (College of William & Mary) DTSTART:20251113T190000Z DTEND:20251113T200000Z DTSTAMP:20260404T111000Z UID:OLS/187 DESCRIPTION:Title: Measuring the Complexity of Countable Models of Presburger Arithmetic \nby Jason Block (College of William & Mary) as part of Online logic s eminar\n\n\nAbstract\nWe examine two methods for classifying the complexit y of countable structures: degree spectra\, and Scott analysis. Degree spe ctra measure how difficult it is to compute copies of structures\, while S cott analysis measures the complexity of describing structures up to isomo rphism. We examine the possible degree spectra and Scott complexities of c ountable Presburger groups and compare these results with those for models of Peano Arithmetic. We also discuss how these measures of complexity suc ceed/fail in distinguishing the intended model of the theory.\n LOCATION:https://stable.researchseminars.org/talk/OLS/187/ END:VEVENT BEGIN:VEVENT SUMMARY:Jeremy Alm (Southern Illinois University) DTSTART:20251002T180000Z DTEND:20251002T190000Z DTSTAMP:20260404T111000Z UID:OLS/188 DESCRIPTION:Title: Relation Algebra and Sumset Problems in Abelian Groups\nby Jeremy Alm (Southern Illinois University) as part of Online logic seminar\n\n\nA bstract\nAn abstract relation algebra (RA) is called representable if it e mbeds in a collection of binary relations closed under union\, complementa tion\, composition\, conversion\, and identity. The question of representa bility is undecidable for finite RAs. It is therefore of interest to impos e various restrictions on the RAs or on the representations themselves in order to narrow the search space. \n\nFor example\, one might consider onl y so-called "cyclic" representations\, which affords a log-quadratic impro vement in search time. If we further assume that the automorphism group of the algebra A with c "colors" (symmetric diversity atoms) contains a cycl e of length c\, and consider only those cyclic representations that arise via a finite field method (due to Comer)\, we actually get decidability: we can check for Comer representations of A in O(c^8 / log c) time. \n\nIf an RA A has no 3-cycles ("rainbow triangles")\, then representability of A is decidable without restriction on the "type" of representation\, a res ult due to Maddux. \n\nA "Goldilocks" happy medium might be found by restr icting attention to representations over abelian groups more generally. I n this context\, problems can be stated in terms of sumset conditions for partitions of the group. For example\,\n\nFor which finite abelian G does there exist a partition G = {0} u A u B such that\n\n\n\n\nThis formulation has two real advanta ges: first\, the problem is understandable to any mathematician\; second\, we can bring in results from the additive number theory literature. \n\nN otice that the set B above is a sum-free set. Constructing sum-free sets with other desired properties is difficult in general. We will discuss thi s in the context of a problem I've been working on for almost 20 years.\n LOCATION:https://stable.researchseminars.org/talk/OLS/188/ END:VEVENT BEGIN:VEVENT SUMMARY:Yatir Halevi (Technion - Israel Institute of Technology) DTSTART:20251120T190000Z DTEND:20251120T200000Z DTSTAMP:20260404T111000Z UID:OLS/189 DESCRIPTION:Title: Around Taylor’s Conjecture and Model-Theoretic Tameness\nby Yat ir Halevi (Technion - Israel Institute of Technology) as part of Online lo gic seminar\n\n\nAbstract\nGiven a graph (G\, E)\, its chromatic number is the smallest cardinal\n$\\kappa$ admitting a legal coloring of the vertic es.\nThe strong Taylor's conjecture states the following:\n\nIf G is an i nfinite graph with chromatic number $\\geq \\aleph_1$\, then\nit contains all finite subgraphs of $Sh_n(\\omega)$ for some n\,\nwhere $Sh_n(\\omega) $ is the n-shift graph (which we will introduce).\n\nThe conjecture was di sproved by Hajnal and Komjáth\; however\, a variant\nof it still holds fo r $\\omega$-stable\, superstable\, or stable graphs.\nOne can also restric t the conjecture and ask when G contains all\nfinite subgraphs of the comp lete graph.\nWe give answers to this question when the edge relation of th e graph\nis stable or when the graph itself is simple.\n\nJoint work with Itay Kaplan and Saharon Shelah\n LOCATION:https://stable.researchseminars.org/talk/OLS/189/ END:VEVENT BEGIN:VEVENT SUMMARY:Gilda Ferreira (Universidade Aberta and CEMS UL) DTSTART:20260115T190000Z DTEND:20260115T200000Z DTSTAMP:20260404T111000Z UID:OLS/190 DESCRIPTION:Title: From Commuting Conversions to Syntactic Identity\nby Gilda Ferrei ra (Universidade Aberta and CEMS UL) as part of Online logic seminar\n\n\n Abstract\nCommuting conversions are often regarded as the "price to pay'' for sequential syntax in natural deduction proofs or even as a sign of ``s yntactic inadequacy''. This presentation explores translations of the Intu itionistic Propositional Calculus (IPC) into systems with no commuting con versions.\n\nAn example of such translations is the well-known Russell-Pra witz translation which maps IPC into a highly expressive system known as S ystem F\, or polymorphic lambda calculus. Despite the elegance of this emb edding\, it fails to preserve proof reduction or even proof identity.\n\nW e will explore two different strategies for achieving proof identity prese rvation. The first strategy involves replacing System F with an atomic pol ymorphic target system. We will present and compare different versions of the Russell-Prawitz translation that follow this strategy [1\,2\,3]. The s econd strategy consists of introducing new atomization conversions to Syst em F [4]\, obtaining not only proof identity preservation but also reducti on preservation.\n\nA recently developed translation [5]\, which completel y avoids commuting conversions\, shows that via the first strategy we can also achieve reduction preservation. Moreover\, this new translation maps commuting conversions to syntactic identity\, achieving a cleaner\, ``comm uting-conversion-free'' image of IPC.\n\nThis presentation includes signif icant joint work with José Espírito Santo.\n\n1. F. Ferreira\, G. Ferrei ra\, Atomic polymorphism\, The Journal of Symbolic Logic\, 78(1)\, pp. 260 -274\, 2013.\n\n2. P. Pistone\, L. Tranchini\, M. Petrolo\, The naturality of natural deduction (II): On atomic polymorphism and generalized proposi tional connectives\, Studia Logica\, 110\, pp. 545-592\, 2022.\n\n3. J. Es pírito Santo\, G. Ferreira\, A refined interpretation of intuitionistic l ogic by means of atomic polymorphism\, Studia Logica\, 108\, pp. 477-507\, 2020.\n\n4. J. Espírito Santo\, G. Ferreira\, The Russell-Prawitz embedd ing and the atomization of universal instantiation\, Logic Journal of the IGPL\, 29(5)\, pp. 823-858\, 2021.\n\n5. J. Espírito Santo\, G. Ferreira\ , How to avoid the commuting conversions of IPC\, Theoretical Computer Sci ence\, 1033\, 2025\n LOCATION:https://stable.researchseminars.org/talk/OLS/190/ END:VEVENT BEGIN:VEVENT SUMMARY:Mathieu Hoyrup (LORIA) DTSTART:20250911T180000Z DTEND:20250911T190000Z DTSTAMP:20260404T111000Z UID:OLS/191 DESCRIPTION:Title: Computable type: an overview\nby Mathieu Hoyrup (LORIA) as part o f Online logic seminar\n\n\nAbstract\nA compact metrizable space X has com putable type if for every set that is homeomorphic to X\, semicomputabilit y is equivalent to computability. This notion was first studied by Joe Mil ler in 2002\, who showed that finite-dimensional spheres all have computab le type. It was then developed by Zvonko Iljazović and his co-authors\, w ho showed among many other results that compact manifolds also enjoy this property. I will present recent results on the notion of computable type\, obtained in collaboration with Djamel Eddine Amir during his PhD\, such a s: a simple characterization of 2-dimensional simplicial complexes having computabe type\, a proof that this property is not preserved by taking bin ary products.\n LOCATION:https://stable.researchseminars.org/talk/OLS/191/ END:VEVENT BEGIN:VEVENT SUMMARY:Xiang Yin (Imperial College London) DTSTART:20251023T180000Z DTEND:20251023T190000Z DTSTAMP:20260404T111000Z UID:OLS/192 DESCRIPTION:Title: On explaining Quantitative Bipolar Argumentation Frameworks\nby X iang Yin (Imperial College London) as part of Online logic seminar\n\n\nAb stract\nQuantitative Bipolar Argumentation Frameworks (QBAFs) provide a po werful tool for modeling reasoning in various applications such as recomme nder systems and fraud detection. However\, there is limited work on expla ining their numerical reasoning outcomes in a systematic way. In this talk \, I will present three novel explanation methods tailored for QBAFs. Firs t\, Argument Attribution Explanations (AAEs) quantify how much each argume nt contributes to a given outcome. Second\, Relation Attribution Explanati ons (RAEs) shift the focus from explaining the influence of arguments to t he support and attack relations\, offering a more fine-grained view of the reasoning process. Third\, Counterfactual Explanations (CEs) identify cha nges to the base scores of the arguments that would lead to a different bu t more desired outcome\, supporting actionable insights and contestability .\n LOCATION:https://stable.researchseminars.org/talk/OLS/192/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabriel Goldberg (University of California Berkeley) DTSTART:20251204T190000Z DTEND:20251204T200000Z DTSTAMP:20260404T111000Z UID:OLS/193 DESCRIPTION:by Gabriel Goldberg (University of California Berkeley) as pa rt of Online logic seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/OLS/193/ END:VEVENT BEGIN:VEVENT SUMMARY:Emma Dinowitz (City University of New York) DTSTART:20251030T180000Z DTEND:20251030T190000Z DTSTAMP:20260404T111000Z UID:OLS/194 DESCRIPTION:Title: A point to set principle for topological entropy and applications to relating dimension\, entropy\, and Lyapunov exponents\nby Emma Dinowit z (City University of New York) as part of Online logic seminar\n\n\nAbstr act\nWe prove a point to set principle for topological entropy by extendin g the orbit complexity framework established by Galatolo\, Hoyrup\, and Ro jas. We use this to establish some classical results in dynamical systems relating dimension\, entropy\, and Lyapunov exponents\, and prove several new dimension formulas in the setting of nonuniformly hyperbolic dynamical systems.\n LOCATION:https://stable.researchseminars.org/talk/OLS/194/ END:VEVENT BEGIN:VEVENT SUMMARY:Garrett Ervin (Eötvös Loránd University) DTSTART:20260312T180000Z DTEND:20260312T190000Z DTSTAMP:20260404T111000Z UID:OLS/195 DESCRIPTION:Title: New arithmetic laws for order types\nby Garrett Ervin (Eötvös L oránd University) as part of Online logic seminar\n\n\nAbstract\nLet (LO\ , +) denote the class of linear orders equipped with the operation of orde red sum (i.e. concatenation). Despite the enormous diversity of linear ord er types\, arithmetic in (LO\, +) is surprisingly nice in certain respects : Lindenbaum showed that (LO\, +) satisfies a completely general Euclidean division theorem\, and Aronszajn found an elegant structural characteriza tion of the commuting pairs in (LO\, +). Yet although these theorems gener alize basic facts about sums of natural numbers\, the published proofs are somewhat difficult and ad hoc. \n\nIn recent work with Eric Paul\, we dev elop a systematic approach to the arithmetic of (LO\, +) by adapting a str ucture theory for group actions on linear orders due to McCleary and other s. Using this approach\, we give new\, unified proofs of Lindenbaum’s an d Aronszajn’s theorems. We then generalize this approach to semigroups a cting by convex embeddings on linear orders\, obtain an arithmetic charact erization of commutativity in (LO\, +)\, and determine exactly the commuta tive semigroups that can be represented in (LO\, +). I will give an overvi ew of our work\, outline some of the proofs\, and discuss future direction s.\n LOCATION:https://stable.researchseminars.org/talk/OLS/195/ END:VEVENT BEGIN:VEVENT SUMMARY:Adrian Mathias DTSTART:20260122T190000Z DTEND:20260122T200000Z DTSTAMP:20260404T111000Z UID:OLS/196 DESCRIPTION:Title: Iteration Problems in Symbolic Dynamics I\nby Adrian Mathias as p art of Online logic seminar\n\n\nAbstract\nFind abstract and handouts at < a href="http://lagrange.math.siu.edu/calvert/OnlineLogicSeminar.html">http ://lagrange.math.siu.edu/calvert/OnlineLogicSeminar.html.\n LOCATION:https://stable.researchseminars.org/talk/OLS/196/ END:VEVENT BEGIN:VEVENT SUMMARY:Linda Lawton (Northern Mighigan University) DTSTART:20260319T180000Z DTEND:20260319T190000Z DTSTAMP:20260404T111000Z UID:OLS/197 DESCRIPTION:Title: Decidability of the AE Theory of $\\Pi^0_1$ Classes$^*$\nby Linda Lawton (Northern Mighigan University) as part of Online logic seminar\n\n \nAbstract\nClick here for abstract\n LOCATION:https://stable.researchseminars.org/talk/OLS/197/ END:VEVENT BEGIN:VEVENT SUMMARY:Sara Riva (Université de Lille) DTSTART:20260129T190000Z DTEND:20260129T200000Z DTSTAMP:20260404T111000Z UID:OLS/198 DESCRIPTION:Title: Control and synthesis of minimal trap spaces in Boolean Network\n by Sara Riva (Université de Lille) as part of Online logic seminar\n\n\nA bstract\nSince recent years\, we observe a surge of successful application s of Boolean networks (BNs) in biology and medicine for the modeling and p rediction of cellular dynamics in the case of cancer and cellular reprogra mming. Such applications face two main challenges: being able to design a qualitative Boolean model which is faithful to the behavior of the biologi cal system and being able to compute predictions to control its (long-term ) dynamics. From a computational point of view\, the latter problem mostly depends on the complexity of the dynamical property to enforce\, while th e former additionally suffers from the combinatorics of candidate models.\ n\nMinimal trap spaces (MTSs) capture subspaces in which the Boolean dynam ics is trapped\, whatever the update mode. They correspond to the attracto rs of the most permissive mode. Due to their versatility\, the computation of MTSs has recently gained traction\, essentially by focusing on their e numeration. We address the logical reasoning on universal properties of MT Ss in the scope of two problems: the reprogramming of Boolean networks for identifying the permanent freeze of Boolean variables that enforce a give n property on all the MTSs\, and the synthesis of Boolean networks from un iversal properties on their MTSs. Both problems reduce to solving the sati sfiability of quantified propositional logic formula with 3 levels of quan tifiers.\n LOCATION:https://stable.researchseminars.org/talk/OLS/198/ END:VEVENT BEGIN:VEVENT SUMMARY:Talk Canceled DTSTART:20260205T190000Z DTEND:20260205T200000Z DTSTAMP:20260404T111000Z UID:OLS/199 DESCRIPTION:Title: Talk Canceled\nby Talk Canceled as part of Online logic seminar\n \n\nAbstract\nWhat does it mean that an event C ``actually caused'' event E?\nThe problem of defining actual causation goes beyond mere philosophica l\nspeculation. For example\, in many legal arguments\, it is precisely w hat\nneeds to be established in order to determine responsibility. (What exactly\nwas the actual cause of the car accident or the medical problem?) \nThe philosophy literature has been struggling with the problem\nof defin ing causality since the days of Hume\, in the 1700s.\nMany of the definiti ons have been couched in terms of counterfactuals.\n(C is a cause of E if\ , had C not happened\, then E would not have happened.)\nIn 2001\, Judea P earl and I introduced a new definition of actual cause\,\nusing Pearl's no tion of structural equations to model\ncounterfactuals. The definition ha s been revised twice since then\,\nextended to deal with notions like "res ponsibility" and "blame"\, and\napplied in databases and program verificat ion. I survey\nthe last 15 years of work here\, including joint work\nwit h Judea Pearl\, Hana Chockler\, and Chris Hitchcock. The talk will be\nco mpletely self-contained.\n LOCATION:https://stable.researchseminars.org/talk/OLS/199/ END:VEVENT BEGIN:VEVENT SUMMARY:Janani Lakshmanan (University of Hawai'i) DTSTART:20260507T180000Z DTEND:20260507T190000Z DTSTAMP:20260404T111000Z UID:OLS/200 DESCRIPTION:by Janani Lakshmanan (University of Hawai'i) as part of Online logic seminar\n\nInteractive livestream: https://zoom.us/j/122323340\nAbs tract: TBA\n LOCATION:https://stable.researchseminars.org/talk/OLS/200/ URL:https://zoom.us/j/122323340 END:VEVENT BEGIN:VEVENT SUMMARY:Hongyu Zhu (University of Wisconsin) DTSTART:20260326T180000Z DTEND:20260326T190000Z DTSTAMP:20260404T111000Z UID:OLS/201 DESCRIPTION:Title: A Complete Bounded Theory with Unbounded Types\nby Hongyu Zhu (Un iversity of Wisconsin) as part of Online logic seminar\n\n\nAbstract\nSay a first-order theory is bounded if for some finite $n$\, it is $\\forall_n $-axiomatizable\; Similarly for a type. This notion is closely related to descriptive complexity and provides a measure of complexity for theories a nd types. In an attempt to connect the complexity of theories and that of their types\, we show the existence of a bounded (in fact universal) theor y which has an unbounded type. The construction uses trees\, and one key s tep of the proof is showing the pseudofiniteness of finite-height trees.\n LOCATION:https://stable.researchseminars.org/talk/OLS/201/ END:VEVENT BEGIN:VEVENT SUMMARY:Dhruv Kulshreshtha (University of Wisconsin) DTSTART:20260305T190000Z DTEND:20260305T200000Z DTSTAMP:20260404T111000Z UID:OLS/202 DESCRIPTION:Title: Surjective cardinals and dually Dedekind finite sets\nby Dhruv Ku lshreshtha (University of Wisconsin) as part of Online logic seminar\n\n\n Abstract\nAssuming the axiom of choice\, cardinal arithmetic is extremely well-behaved: any two sets are comparable in size\, and there is no infini te strictly decreasing sequence of cardinals. Moreover\, for any nonempty sets X and Y\, X injects into Y if and only if Y surjects onto X—so the injective and surjective "orderings" coincide. Without choice\, much of th is structure breaks down: there may exist incomparable sets and infinite s trictly decreasing sequences of cardinals. Although the Cantor-Schröder-B ernstein theorem ensures that if two sets inject into each other then they are in bijective correspondence\, no analogous result need hold for surje ctions\, so the injective and surjective orderings may also no longer agre e. In this talk\, we examine the surjective ordering on sets in the absenc e of choice\, focusing on results that highlight just how bad the situatio n can be. We also discuss some results surrounding the surjective well-fou ndedness of cardinals. We draw on recent works of Shen and Zhou and on joi nt work of the speaker with Andreas Blass.\n LOCATION:https://stable.researchseminars.org/talk/OLS/202/ END:VEVENT BEGIN:VEVENT SUMMARY:Jorge Cruz Chapital (University of Trononto) DTSTART:20260212T190000Z DTEND:20260212T200000Z DTSTAMP:20260404T111000Z UID:OLS/203 DESCRIPTION:Title: Construction schemes: Finitizations of guessing principles and their parametrized forcing axioms.\nby Jorge Cruz Chapital (University of Tr ononto) as part of Online logic seminar\n\n\nAbstract\nIn this talk\, we s urvey recent developments in the theory of capturing schemes introduced by Todorcevic. We present the capturing axioms CAρ​\, CAΔ​\, and CA\, which may be viewed as finite-dimensional analogues of the classical guess ing principles Club\, CH\, and Diamond\, respectively. We show that many c onsequences traditionally derived from these guessing principles already f ollow from the capturing axioms\, often with significantly simpler proofs. Finally\, we introduce parametrized forcing axioms naturally associated w ith the capturing principles and demonstrate how they can be used to estab lish the independence of a strong statement about gaps over ω\, a problem that cannot be settled using either traditional guessing principles or st andard forcing axioms.\n LOCATION:https://stable.researchseminars.org/talk/OLS/203/ END:VEVENT BEGIN:VEVENT SUMMARY:Adrian Mathias DTSTART:20260219T190000Z DTEND:20260219T200000Z DTSTAMP:20260404T111000Z UID:OLS/204 DESCRIPTION:Title: Iteration problems in symbolic dynamics II\nby Adrian Mathias as part of Online logic seminar\n\n\nAbstract\nFind abstract and handouts at htt p://lagrange.math.siu.edu/calvert/OnlineLogicSeminar.html.\n LOCATION:https://stable.researchseminars.org/talk/OLS/204/ END:VEVENT BEGIN:VEVENT SUMMARY:Christian Rosendal (University of Maryland) DTSTART:20260226T190000Z DTEND:20260226T200000Z DTSTAMP:20260404T111000Z UID:OLS/205 DESCRIPTION:Title: Coordinate systems in Banach spaces and lattices via descriptive set theory\nby Christian Rosendal (University of Maryland) as part of Onli ne logic seminar\n\n\nAbstract\nUsing methods of descriptive set theory\, we answer several questions from the literature regarding different notion s of infinite bases in Banach lattices. In particular\, under the assumpti on of analytic determinacy\, every σ-order basis (e_n) for a Banach latti ce X=[e_n] is a uniform basis\, and every uniform basis is Schauder. Regar ding Banach spaces\, we consider filter Schauder bases for Banach spaces\, i.e.\, in which the norm convergence of partial sums is replaced by norm convergence along some appropriate filter on ℕ. We show that every filte r Schauder basis with respect to an analytic filter is also a filter Schau der basis with respect to a Borel filter. The talk is accessible to a gene ral logic audience. This is joint work with Antonio Aviles\, Mitchell Tayl or and Pedro Tradacete.\n LOCATION:https://stable.researchseminars.org/talk/OLS/205/ END:VEVENT BEGIN:VEVENT SUMMARY:John Baldwin (University of Illinois Chicago) DTSTART:20260402T180000Z DTEND:20260402T190000Z DTSTAMP:20260404T111000Z UID:OLS/206 DESCRIPTION:Title: Categoricity for the inferential $\\omega$-logic and $L_{\\omega_1\\o mega}$\nby John Baldwin (University of Illinois Chicago) as part of On line logic seminar\n\n\nAbstract\nAbstract available on seminar web page a t h ttp://lagrange.math.siu.edu/calvert/OnlineLogicSeminar.html\n LOCATION:https://stable.researchseminars.org/talk/OLS/206/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabriela Laboska (Northwestern University) DTSTART:20260430T180000Z DTEND:20260430T190000Z DTSTAMP:20260404T111000Z UID:OLS/207 DESCRIPTION:by Gabriela Laboska (Northwestern University) as part of Onlin e logic seminar\n\nInteractive livestream: https://zoom.us/j/122323340\nAb stract: TBA\n LOCATION:https://stable.researchseminars.org/talk/OLS/207/ URL:https://zoom.us/j/122323340 END:VEVENT BEGIN:VEVENT SUMMARY:Stanislav Srednyak (Duke University) DTSTART:20260409T180000Z DTEND:20260409T190000Z DTSTAMP:20260404T111000Z UID:OLS/208 DESCRIPTION:Title: On logical problems arising in atomic and particle physics\nby St anislav Srednyak (Duke University) as part of Online logic seminar\n\nInte ractive livestream: https://zoom.us/j/122323340\n\nAbstract\nIn this talk\ , I will present certain ideas from quantum field theory that lead to math ematical problems typically addressed in mathematical logic literature. Th is will be an overview talk\, accessible to a general logic audience\, and it will have four main themes:\n\n1) evidence that non computable functio ns arise in dynamics of elementary particles. I will discuss how this non computability can manifest itself in precision measurements and what this means for quantum computing.\n\n2) rigorous definition of path integral. I will formulate the problem in the language of Banach space theory\, and d iscuss relations to recent work on Banach homological algebra.\n\n3) highe r quantizations and higher functionals. I will define a hierarchy of symme tric functionals of low complexity but arbitrarily high in the constructiv e universe\, and show the relevance of this construction to physical obser vables.\n\n4) quantum randomness vs mathematical randomness. I will compar e these two notions of randomness and discuss what is the interplay with t he hierarchies of definable function spaces and the problem in 2) of defin ing integration over function spaces. I will touch upon the measurement pr oblem and its interpretation from a mathematical perspective.\n LOCATION:https://stable.researchseminars.org/talk/OLS/208/ URL:https://zoom.us/j/122323340 END:VEVENT BEGIN:VEVENT SUMMARY:José Jeremías Valenzuela Morales (George Washington University) DTSTART:20260416T180000Z DTEND:20260416T190000Z DTSTAMP:20260404T111000Z UID:OLS/209 DESCRIPTION:Title: A Timeline of Lattice Embeddings into the Turing Degrees\nby Jos é Jeremías Valenzuela Morales (George Washington University) as part of Online logic seminar\n\nInteractive livestream: https://zoom.us/j/12232334 0\n\nAbstract\nThe Turing degrees form a rich upper semilattice. As such\, a natural way to explore their structure is by studying which types of se milattices can be embedded into them. From Kleene-Post's embeddability res ult for finite upper semilattices\, to Lerman's embeddability criterion an d Montalbán's work on jump upper semilattices\, this expository talk will survey several classic embedding results with a focus on their techniques and machinery.\n LOCATION:https://stable.researchseminars.org/talk/OLS/209/ URL:https://zoom.us/j/122323340 END:VEVENT BEGIN:VEVENT SUMMARY:Henry Klatt (George Washington University) DTSTART:20260423T180000Z DTEND:20260423T190000Z DTSTAMP:20260404T111000Z UID:OLS/210 DESCRIPTION:by Henry Klatt (George Washington University) as part of Onlin e logic seminar\n\nInteractive livestream: https://zoom.us/j/122323340\nAb stract: TBA\n LOCATION:https://stable.researchseminars.org/talk/OLS/210/ URL:https://zoom.us/j/122323340 END:VEVENT END:VCALENDAR