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:20260422T212607Z UID:FieldsSetTheory/1 DESCRIPTION:Title: A Decomposition Theorem for Aronszajn Lines\nby Keegan Dasilva Barbosa (University of Toronto) as part of Toronto set theory seminar\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 em beddability relation. In particular\, we show that the class of better qua si order labeled fragmented Aronszajn lines is itself a better quasi order . Moreover\, we show that every better quasi order labeled Aronszajn line can be expressed as a finite sum of labeled types which are algebraically indecomposable. By encoding lines with finite labeled trees\, we are also able to deduce a decomposition result\, that for every Aronszajn line $L$\ , 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 t han $n$ colours. \n LOCATION:https://researchseminars.org/talk/FieldsSetTheory/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Matteo Viale (University of Torino) DTSTART:20200417T173000Z DTEND:20200417T183000Z DTSTAMP:20260422T212607Z 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 (assum ing large cardinals) set theory is a tractable (and we dare to say tame) f irst order theory when formalized in a first order signature with natural predicate symbols for the basic definable concepts of second and third ord er arithmetic\, and appealing to the model-theoretic notions of model comp leteness and model companionship.\n\nSpecifically we develop a general fra mework linking generic absoluteness results to model companionship and sho w that (with the required care in details) a $\\Pi_2$-property formalized in an appropriate language for second or third order number theory is forc ible from some T extending ZFC + large cardinals if and only if it is cons istent with the universal fragment of T if and only if it is realized in t he model companion of T.\n\nPart (but not all) of our results are conditio nal to the proof of Schindler and Asperò that Woodin's axiom (*) can be f orced by a stationary set preserving forcing.\n LOCATION:https://researchseminars.org/talk/FieldsSetTheory/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Todd Eisworth (Ohio State University) DTSTART:20200424T173000Z DTEND:20200424T183000Z DTSTAMP:20260422T212607Z UID:FieldsSetTheory/3 DESCRIPTION:Title: Representability and pseudopowers\nby Todd Eisworth (Ohio Stat e University) as part of Toronto set theory seminar\n\n\nAbstract\nWe will prove some basic facts about Shelah's pseudopower function\, and derive s ome new (?) ZFC results in cardinal arithmetic using basic topological ide as. This talk is designed to be an introduction to this part of pcf theory .\n LOCATION:https://researchseminars.org/talk/FieldsSetTheory/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Szeptycki (York University) DTSTART:20200501T173000Z DTEND:20200501T183000Z DTSTAMP:20260422T212607Z UID:FieldsSetTheory/4 DESCRIPTION:Title: Strong convergence properties and an example from a $\\Box$ sequen ce\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://researchseminars.org/talk/FieldsSetTheory/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Dima Sinapova (UIC) DTSTART:20200508T173000Z DTEND:20200508T183000Z DTSTAMP:20260422T212607Z UID:FieldsSetTheory/5 DESCRIPTION:Title: Iteration\, reflection\, and Prikry forcing.\nby Dima Sinapova (UIC) as part of Toronto set theory seminar\n\n\nAbstract\nThere is an in herent tension between stationary reflection and the failure of SCH. The f ormer is a compactness type principle that follows from large cardinals. T he latter is an instance of incompactness\, and usually obtained using Pri kry forcing. We describe a Prikry style iteration\, and use it to force st ationary reflection in the presence of not SCH. Then we discuss the situat ion at smaller cardinals. This is joint work with Alejandro Poveda and Ass af Rinot.\n LOCATION:https://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:20260422T212607Z UID:FieldsSetTheory/6 DESCRIPTION:Title: Pseudocompact hyperspaces of Isbell-Mrówka spaces\nby Viniciu s de Oliveira Rodrigues (University of São Paulo and University of São P aulo\, Institute of Mathematics and Statistics) as part of Toronto set the ory seminar\n\n\nAbstract\nJ. Ginsburg has asked what is the relation betw een the pseudocompactness of the $\\omega$-th power of a topological space $X$ and the pseudocompactness of its Vietoris Hyperspace\, $\\exp(X)$. M. Hrusak\, I. Martínez-Ruiz and F. Hernandez-Hernandez studied this questi on restricted to Isbell-Mrówka spaces\, that is\, spaces of the form $\\P si(A)$ 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 that if the cardinal characteristic $\\mathfrak{p}$ is $\\mathfrak{c}$\, then for every MAD family $A$\, $\\exp(\\Psi(A))$ is pseudocompact\, and if the car dinal characteristic $\\mathfrak{h}$ is less than $\\mathfrak{c}$\, there exists a MAD family $A$ such that $\\exp(\\Psi(A))$ is not pseudocompact. They asked if there exists a MAD family $A$ (in ZFC) such that $\\exp(\\Ps i(A))$ is pseudocompact.\n\nIn this talk\, we present some new results on the (consistent) existence of MAD families whose hyperspaces of their Isbe ll-Mrówka spaces are (or are not) pseudocompact by constructing new examp les. Moreover\, we give some combinatorial equivalences for every Isbell-M rówka space from a MAD family having pseudocompact hyperspace. This is a joint work with\, O. Guzman\, M. Hrusak\, S. Todorcevic and A. Tomita.\n LOCATION:https://researchseminars.org/talk/FieldsSetTheory/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Jamal Kawach (University of Toronto) DTSTART:20200612T173000Z DTEND:20200612T183000Z DTSTAMP:20260422T212607Z UID:FieldsSetTheory/7 DESCRIPTION:Title: Dual Ramsey theory for countable ordinals\nby Jamal Kawach (Un iversity of Toronto) as part of Toronto set theory seminar\n\n\nAbstract\n Using techniques from the theory of topological Ramsey spaces\, we prove a dual Ramsey theorem for countable ordinals. Specifically\, for each count able ordinal $\\alpha$ we define a topological Ramsey space of equivalence relations on $\\omega$ which code equivalence relations on $\\alpha$\, up to a necessary restriction on the set of minimal representatives of the e quivalence classes. This extends the classical dual Ramsey theorem of Carl son and Simpson. This is joint work with Stevo Todorcevic.\n LOCATION:https://researchseminars.org/talk/FieldsSetTheory/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Will Brian (University of North Carolina at Charlotte) DTSTART:20200626T173000Z DTEND:20200626T183000Z DTSTAMP:20260422T212607Z UID:FieldsSetTheory/8 DESCRIPTION:Title: Limited-information strategies in Banach-Mazur games\nby Will Brian (University of North Carolina at Charlotte) as part of Toronto set t heory seminar\n\n\nAbstract\nThe Banach-Mazur game is an infinite-length g ame played on a topological space X\, in which two players take turns choo sing members of an infinite decreasing sequence of open sets\, the first p layer trying to ensure that the intersection of this sequence is empty\, a nd the second that it is not. A limited-information strategy for one of th e players is a game plan that\, on any given move\, depends on only a smal l part of the game's history. In this talk we will discuss Telgársky's co njecture\, which asserts roughly that there must be topological spaces whe re winning strategies for the Banach-Mazur game cannot be too limited\, bu t must rely on large parts of the game's history in a significant way. Rec ently\, it was shown that this conjecture fails in models of set theory sa tisfying GCH + $\\Box$. In such models it is always possible for one playe r to code all information concerning a game's history into a small piece o f it. We will discuss these so-called coding strategies\, why assuming GCH + $\\Box$ makes them work so well\, and what can go wrong in other models of set theory.\n LOCATION:https://researchseminars.org/talk/FieldsSetTheory/8/ END:VEVENT END:VCALENDAR