BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Juan Aguilera (Ghent University) DTSTART:20211215T163000Z DTEND:20211215T173000Z DTSTAMP:20260404T100027Z UID:Bristol-logic-and-set-theory/1 DESCRIPTION:Title: The Pi12 Consequences of a Theory\nby Juan Aguilera (Ghent University) as part of Bristol Logic and Set Theory Semin ar\n\n\nAbstract\nWe define the \\Pi^1_2-norm |T| of a theory T\, an analo gue of the proof-theoretic ordinal of T for statements of complexity \\Pi^ 1_2. We go over the basic theory of |T| and use it to define the \\Pi^1_2- soundness ordinal of T. Then\, we characterise the recursive and admissibl e ordinals which are \\Pi^1_2-soundness ordinals of some recursively enume rable extension of Arithmetical Comprehension. This is joint work with Fed or Pakhomov.\n LOCATION:https://stable.researchseminars.org/talk/Bristol-logic-and-set-th eory/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Tanmay Inamdar (Bar-Ilan University) DTSTART:20220616T140000Z DTEND:20220616T153000Z DTSTAMP:20260404T100027Z UID:Bristol-logic-and-set-theory/2 DESCRIPTION:Title: From Sierpinski-type colourings to Ulam-type m atrices\nby Tanmay Inamdar (Bar-Ilan University) as part of Bristol Lo gic and Set Theory Seminar\n\n\nAbstract\nUlam matrices were introduced by Ulam in his study of the measure problem. Ulam's construction applies to all successor cardinals Kappa\, and later Hajnal extended the construction to apply to some limit cardinals as well. In my talk I will show how a co louring principle introduced by Sierpinski can be used to construct matric es with similar applications as the matrices of Ulam and Hajnal. I will al so show how such colouring principles can be obtained from the existence o f a non-trivial C-sequence on Kappa using walks on ordinals. As a conseque nce\, the resulting matrices are more readily available than the matrices of Ulam and Hajnal. The results I present are joint work with Assaf Rinot. \n LOCATION:https://stable.researchseminars.org/talk/Bristol-logic-and-set-th eory/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Will Stafford (University of Bristol) DTSTART:20220929T113000Z DTEND:20220929T123000Z DTSTAMP:20260404T100027Z UID:Bristol-logic-and-set-theory/3 DESCRIPTION:Title: Is the Proof-Theoretically Valid Logic Intuiti onistic?\nby Will Stafford (University of Bristol) as part of Bristol Logic and Set Theory Seminar\n\n\nAbstract\nSeveral recent results bring i nto focus the superintuitionistic nature of most notions of proof-theoreti c validity\, but little work has been done evaluating the consequences of these results. Proof-theoretic validity claims to offer a formal explicati on of how inferences follow from the definitions of logic connectives (whi ch are defined by their introduction rules). This paper explores whether t he new results undermine this claim. It is argued that\, while the formal results are worrying\, superintuitionistic inferences are valid because th e treatments of atomic formulas are insufficiently general\, and a resolut ion to this issue is proposed.\n LOCATION:https://stable.researchseminars.org/talk/Bristol-logic-and-set-th eory/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Frank Stephan (National University of Singapore) DTSTART:20221020T093000Z DTEND:20221020T103000Z DTSTAMP:20260404T100027Z UID:Bristol-logic-and-set-theory/4 DESCRIPTION:Title: Initial Segment Complexity for Measures\nb y Frank Stephan (National University of Singapore) as part of Bristol Logi c and Set Theory Seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/Bristol-logic-and-set-th eory/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Sean Cox (Virginia Commonwealth University) DTSTART:20221101T123000Z DTEND:20221101T133000Z DTSTAMP:20260404T100027Z UID:Bristol-logic-and-set-theory/5 DESCRIPTION:Title: Homological algebra\, elementary submodels\, a nd stationary logic\nby Sean Cox (Virginia Commonwealth University) as part of Bristol Logic and Set Theory Seminar\n\n\nAbstract\nThe talk will focus on the use of set-theoretic elementary submodel techniques to solve \, or partially solve\, some problems from homological algebra (independen ce of Salce's Problem about cotorsion pairs\, and the precovering problem in Gorenstein Homological Algebra).\n LOCATION:https://stable.researchseminars.org/talk/Bristol-logic-and-set-th eory/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Sam Coskey (Boise State University) DTSTART:20221115T123000Z DTEND:20221115T133000Z DTSTAMP:20260404T100027Z UID:Bristol-logic-and-set-theory/6 DESCRIPTION:Title: Jumps in the Borel complexity hierarchy\nb y Sam Coskey (Boise State University) as part of Bristol Logic and Set The ory Seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/Bristol-logic-and-set-th eory/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Minh Tran (National University of Singapore) DTSTART:20230308T163000Z DTEND:20230308T173000Z DTSTAMP:20260404T100027Z UID:Bristol-logic-and-set-theory/7 DESCRIPTION:Title: Toward classifying the reducts of the complex fields\nby Minh Tran (National University of Singapore) as part of Bri stol Logic and Set Theory Seminar\n\n\nAbstract\nWe will discuss some rece nt progress on the problem of classifying the reducts of the complex field (with named parameters and up to interdefinability). The tools we use inc lude the recent solutions of the Restricted Trichotomy Conjecture in chara cteristic 0 and a generalized sumproduct result from additive combinatoric s. (Joint with Benjamin Castle)\n LOCATION:https://stable.researchseminars.org/talk/Bristol-logic-and-set-th eory/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Juan Aguilera (University og Ghent) DTSTART:20230322T140000Z DTEND:20230322T153000Z DTSTAMP:20260404T100027Z UID:Bristol-logic-and-set-theory/8 DESCRIPTION:Title: A generalization of Borel determinacy\nby Juan Aguilera (University og Ghent) as part of Bristol Logic and Set Theor y Seminar\n\n\nAbstract\nWe present a theorem which is\, in some sense\, t he provably optimal generalization of Martin's Borel determinacy for infin ite games on integers. \n\nPlease see below or the seminar webpage https:/ /www.bristolmathsresearch.org/seminar/juan-aguilera-3 for the zoom link.\n LOCATION:https://stable.researchseminars.org/talk/Bristol-logic-and-set-th eory/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Beatrice Pitton (University of Lausanne) DTSTART:20230523T123000Z DTEND:20230523T133000Z DTSTAMP:20260404T100027Z UID:Bristol-logic-and-set-theory/9 DESCRIPTION:Title: Definable subsets of the generalized Cantor an d Baire spaces\nby Beatrice Pitton (University of Lausanne) as part of Bristol Logic and Set Theory Seminar\n\n\nAbstract\nGeneralized descripti ve set theory (GDST) aims at developing a higher analogue of classical des criptive set theory in which $\\omega$ is replaced with an uncountable car dinal $\\kappa$ in all definitions and relevant notions. In the literature on GDST it is often required that $\\kappa^{<\\kappa}=\\kappa$\, a condit ion equivalent to κ regular and $2^{<\\kappa}=\\kappa$. In contrast\, in this paper we use a more general approach and develop in a uniform way the basics of GDST for cardinals $\\kappa$ still satisfying $2^{<\\kappa}=\\k appa$ but independently of whether they are regular or singular. This allo ws us to retrieve as a special case the known results for regular $\\kappa $\, but it also uncovers their analogues when $\\kappa$ is singular. We al so discuss some new phenomena specifically arising in the singular context (such as the existence of two distinct yet related Borel hierarchies)\, a nd obtain some results which are new also in the setup of regular cardinal s\, such as the existence of unfair Borel∗ codes for all Borel∗ sets. This is joint work with Luca Motto Ros.\n\nThe zoom link for this talk is https://bristol-ac-uk.zoom.us/j/93185058773.\n LOCATION:https://stable.researchseminars.org/talk/Bristol-logic-and-set-th eory/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Bokai Yao (University of Notre Dame) DTSTART:20230523T140000Z DTEND:20230523T150000Z DTSTAMP:20260404T100027Z UID:Bristol-logic-and-set-theory/10 DESCRIPTION:Title: Forcing with Urelements\nby Bokai Yao (Un iversity of Notre Dame) as part of Bristol Logic and Set Theory Seminar\n\ n\nAbstract\nI will begin by isolating a hierarchy of axioms based on ZFCU _R\, which is ZFC set theory (with Replacement) modified to allow a class of urelements. For example\, the Collection Principle is equivalent to the Reflection Principle over ZFCU_R\, while it is folklore that neither of t hem is provable in ZFCU_R.\n\nI then turn to forcing over countable transi tive models of ZFU_R. A forcing relation is full just in case whenever a f orcing condition p forces an existential statement\, p also forces some in stance of that statement. According to the existing approach\, forcing rel ations are almost never full when there are urelements. I introduce a new forcing machinery to address this problem. I show that over ZFCU_R\, the p rinciple that every new forcing relation is full is equivalent to the Coll ection Principle. Furthermore\, I show how forcing is able to preserve\, d estroy and resurrect the axioms in the hierarchy I introduced. In particul ar\, the Reflection Principle is “necessarily forceble” in certain mod els of ZFCU_R. In the end\, I will consider how the ground model definabil ity can fail when the ground model contains a proper class of urelements.\ n\nThe zoom link for this talk is https://bristol-ac-uk.zoom.us/j/93185058 773.\n LOCATION:https://stable.researchseminars.org/talk/Bristol-logic-and-set-th eory/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Shay Logan (Kansas State University) DTSTART:20231004T150000Z DTEND:20231004T160000Z DTSTAMP:20260404T100027Z UID:Bristol-logic-and-set-theory/11 DESCRIPTION:Title: Varieties of Variable Sharing or: How I Stopp ed Worrying and Learned to Love Nonuniform Substitutions\nby Shay Loga n (Kansas State University) as part of Bristol Logic and Set Theory Semina r\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/Bristol-logic-and-set-th eory/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Jonathan Schilhan (University of Leeds) DTSTART:20231129T153000Z DTEND:20231129T170000Z DTSTAMP:20260404T100027Z UID:Bristol-logic-and-set-theory/12 DESCRIPTION:Title: A geometric condition for Dependent Choice\nby Jonathan Schilhan (University of Leeds) as part of Bristol Logic and Set Theory Seminar\n\nLecture held in G.06 Fry Building.\n\nAbstract\nThe method of permutation models is used to prove basic independence results related to the Axiom of Choice over set theory with atoms. While it is alr eady more than 100 years old (introduced in 1922)\, arguments that show wh ether DC holds in a permutation model have always been either ad-hoc or re lied simply on the filter of groups being countably closed. We have succee ded in crystallising a condition which characterizes precisely when DC hol ds or not. Under some circumstances\, the same characterization still hold s for symmetric extensions.\n LOCATION:https://stable.researchseminars.org/talk/Bristol-logic-and-set-th eory/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Merlin Carl (Europa-Universität Flensburg) DTSTART:20231206T153000Z DTEND:20231206T163000Z DTSTAMP:20260404T100027Z UID:Bristol-logic-and-set-theory/13 DESCRIPTION:Title: Space and time complexity for Infinite Time T uring Machines\nby Merlin Carl (Europa-Universität Flensburg) as part of Bristol Logic and Set Theory Seminar\n\n\nAbstract\nInfinite Time Turi ng Machines (ITTMs)\, defined in the classical paper by Hamkins and Lewis\ , allow Turing machines to run for transfinite ordinal time. One can then generalize notions of time (Schindler) and space (Löwe) complexity to thi s setting. Löwe's "bold conjecture" was whether the two notions are non-t rivially connected\, i.e.\, whether low space complexity implies low time complexity. In our talk\, we will show that this conjecture fails. Showing this will\, however\, leads naturally to a systematic study of decision a nd semi-decision times on ITTMs\, which was done in joint work with Philip p Schlicht and Philip Welch and led to connections with descriptive set th eory and generalizations to the theory of ranks.\n LOCATION:https://stable.researchseminars.org/talk/Bristol-logic-and-set-th eory/13/ END:VEVENT END:VCALENDAR