BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Keegan Dasilva Barbosa (University of Toronto) DTSTART:20200410T173000Z DTEND:20200410T183000Z DTSTAMP:20260404T110742Z UID:FieldsSetTheory/1 DESCRIPTION:Title: A Decomposition Theorem for Aronszajn Lines\nby Keegan Dasilva Barbosa (University of Toronto) as part of Toronto set theory semi nar\n\n\nAbstract\nWe will prove that under the proper forcing axiom\, the class of all Aronszajn lines behave like $\\sigma$-scattered orders under the embeddability relation. In particular\, we show that the class of bet ter quasi order labeled fragmented Aronszajn lines is itself a better quas i order. Moreover\, we show that every better quasi order labeled Aronszaj n line can be expressed as a finite sum of labeled types which are algebra ically indecomposable. By encoding lines with finite labeled trees\, we ar e also able to deduce a decomposition result\, that for every Aronszajn li ne $L$\, there is an $n\\in \\omega$ such that for any finite colouring of $L$\, there is a subset $L\\prime$ of $L$ isomorphic to $L$ which uses no more than $n$ colours. \n LOCATION:https://stable.researchseminars.org/talk/FieldsSetTheory/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Matteo Viale (University of Torino) DTSTART:20200417T173000Z DTEND:20200417T183000Z DTSTAMP:20260404T110742Z UID:FieldsSetTheory/2 DESCRIPTION:Title: Tameness for Set Theory\nby Matteo Viale (University of Torino) as part of Toronto set theory seminar\n\n\nAbstract\nWe show that (assuming large cardinals) set theory is a tractable (and we dare to say tame) first order theory when formalized in a first order signature with n atural predicate symbols for the basic definable concepts of second and th ird order arithmetic\, and appealing to the model-theoretic notions of mod el completeness and model companionship.\n\nSpecifically we develop a gene ral framework linking generic absoluteness results to model companionship and show that (with the required care in details) a $\\Pi_2$-property form alized in an appropriate language for second or third order number theory is forcible from some T extending ZFC + large cardinals if and only if it is consistent with the universal fragment of T if and only if it is realiz ed in the model companion of T.\n\nPart (but not all) of our results are c onditional to the proof of Schindler and Asperò that Woodin's axiom (*) c an be forced by a stationary set preserving forcing.\n LOCATION:https://stable.researchseminars.org/talk/FieldsSetTheory/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Todd Eisworth (Ohio State University) DTSTART:20200424T173000Z DTEND:20200424T183000Z DTSTAMP:20260404T110742Z UID:FieldsSetTheory/3 DESCRIPTION:Title: Representability and pseudopowers\nby Todd Eisworth (Oh io State University) as part of Toronto set theory seminar\n\n\nAbstract\n We will prove some basic facts about Shelah's pseudopower function\, and d erive some new (?) ZFC results in cardinal arithmetic using basic topologi cal ideas. This talk is designed to be an introduction to this part of pcf theory.\n LOCATION:https://stable.researchseminars.org/talk/FieldsSetTheory/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Szeptycki (York University) DTSTART:20200501T173000Z DTEND:20200501T183000Z DTSTAMP:20260404T110742Z UID:FieldsSetTheory/4 DESCRIPTION:Title: Strong convergence properties and an example from a $\\Box$ sequence\nby Paul Szeptycki (York University) as part of Toronto set theory seminar\n\n\nAbstract\nWe present an example of a space constructed from $\\Box(\\kappa)$ answering some questions of Arhangel'skii.\n LOCATION:https://stable.researchseminars.org/talk/FieldsSetTheory/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Dima Sinapova (UIC) DTSTART:20200508T173000Z DTEND:20200508T183000Z DTSTAMP:20260404T110742Z UID:FieldsSetTheory/5 DESCRIPTION:Title: Iteration\, reflection\, and Prikry forcing.\nby Dima S inapova (UIC) as part of Toronto set theory seminar\n\n\nAbstract\nThere i s an inherent tension between stationary reflection and the failure of SCH . The former is a compactness type principle that follows from large cardi nals. The latter is an instance of incompactness\, and usually obtained us ing Prikry forcing. We describe a Prikry style iteration\, and use it to f orce stationary reflection 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/FieldsSetTheory/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Vinicius de Oliveira Rodrigues (University of São Paulo and Unive rsity of São Paulo\, Institute of Mathematics and Statistics) DTSTART:20200522T173000Z DTEND:20200522T183000Z DTSTAMP:20260404T110742Z UID:FieldsSetTheory/6 DESCRIPTION:Title: Pseudocompact hyperspaces of Isbell-Mrówka spaces\nby Vinicius de Oliveira Rodrigues (University of São Paulo and University of São Paulo\, Institute of Mathematics and Statistics) as part of Toronto set theory seminar\n\n\nAbstract\nJ. Ginsburg has asked what is the relati on between the pseudocompactness of the $\\omega$-th power of a topologica l space $X$ and the pseudocompactness of its Vietoris Hyperspace\, $\\exp( X)$. M. Hrusak\, I. Martínez-Ruiz and F. Hernandez-Hernandez studied this question restricted to Isbell-Mrówka spaces\, that is\, spaces of the fo rm $\\Psi(A)$ where A is an almost disjoint family. Regarding these spaces \, if $\\exp(X)$ is pseudocompact\, then $X^\\omega$ is also pseudocompact \, and $X^\\omega$ is pseudocompact iff $A$ is a MAD family. They showed t hat if the cardinal characteristic $\\mathfrak{p}$ is $\\mathfrak{c}$\, th en for every MAD family $A$\, $\\exp(\\Psi(A))$ is pseudocompact\, and if the cardinal characteristic $\\mathfrak{h}$ is less than $\\mathfrak{c}$\, there exists a MAD family $A$ such that $\\exp(\\Psi(A))$ is not pseudoco mpact. They asked if there exists a MAD family $A$ (in ZFC) such that $\\e xp(\\Psi(A))$ is pseudocompact.\n\nIn this talk\, we present some new resu lts on the (consistent) existence of MAD families whose hyperspaces of the ir Isbell-Mrówka spaces are (or are not) pseudocompact by constructing ne w examples. Moreover\, we give some combinatorial equivalences for every I sbell-Mrówka space from a MAD family having pseudocompact hyperspace. Thi s is a joint work with\, O. Guzman\, M. Hrusak\, S. Todorcevic and A. Tomi ta.\n LOCATION:https://stable.researchseminars.org/talk/FieldsSetTheory/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Jamal Kawach (University of Toronto) DTSTART:20200612T173000Z DTEND:20200612T183000Z DTSTAMP:20260404T110742Z UID:FieldsSetTheory/7 DESCRIPTION:Title: Dual Ramsey theory for countable ordinals\nby Jamal Kaw ach (University of Toronto) as part of Toronto set theory seminar\n\n\nAbs tract\nUsing techniques from the theory of topological Ramsey spaces\, we prove a dual Ramsey theorem for countable ordinals. Specifically\, for eac h countable ordinal $\\alpha$ we define a topological Ramsey space of equi valence relations on $\\omega$ which code equivalence relations on $\\alph a$\, up to a necessary restriction on the set of minimal representatives o f the equivalence classes. This extends the classical dual Ramsey theorem of Carlson and Simpson. This is joint work with Stevo Todorcevic.\n LOCATION:https://stable.researchseminars.org/talk/FieldsSetTheory/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Will Brian (University of North Carolina at Charlotte) DTSTART:20200626T173000Z DTEND:20200626T183000Z DTSTAMP:20260404T110742Z UID:FieldsSetTheory/8 DESCRIPTION:Title: Limited-information strategies in Banach-Mazur games\nb y Will Brian (University of North Carolina at Charlotte) as part of Toront o set theory seminar\n\n\nAbstract\nThe Banach-Mazur game is an infinite-l ength game played on a topological space X\, in which two players take tur ns choosing members of an infinite decreasing sequence of open sets\, the first player trying to ensure that the intersection of this sequence is em pty\, and the second that it is not. A limited-information strategy for on e of the players is a game plan that\, on any given move\, depends on only a small part of the game's history. In this talk we will discuss Telgárs ky's conjecture\, which asserts roughly that there must be topological spa ces where winning strategies for the Banach-Mazur game cannot be too limit ed\, but must rely on large parts of the game's history in a significant w ay. Recently\, it was shown that this conjecture fails in models of set th eory satisfying GCH + $\\Box$. In such models it is always possible for on e player to code all information concerning a game's history into a small piece of it. We will discuss these so-called coding strategies\, why assum ing GCH + $\\Box$ makes them work so well\, and what can go wrong in other models of set theory.\n LOCATION:https://stable.researchseminars.org/talk/FieldsSetTheory/8/ END:VEVENT END:VCALENDAR