# Online activities May 11 — May 17 2020

May 12

Münster Set Theory Seminar
Time: Tuesday, May 12, 4:15pm CEST
Speaker: Farmer Schlutzenberg, University of Muenster
Title: $j:V_\delta\to V_\delta$ in $L(V_\delta)$
Abstract: Assuming $\mathrm{ZF}+V=L(V_\delta)$ where $\delta$ is a
limit ordinal of uncountable cofinality, we show there is no
non-trivial $\Sigma_1$-elementary $j:V_\delta\to V_\delta$. Reference:
Section 8 of “Reinhardt cardinals and non-definability”, arXiv
2002.01215.
Information: contact rds@wwu.de ahead of time in order to participate.

Cornell Logic Seminar
Time: Tuesday, May 12, 2:55pm New York time (20:55pm CEST)
Speaker: Konstantin Slutsky, University of Paris 7
Title: Smooth Orbit equivalence relation of free Borel R^d-actions
Abstract: Smooth Orbit Equivalence (SOE) is an orbit equivalence relation between free ℝd-flows that acts by diffeomorphisms between orbits. This idea originated in ergodic theory of ℝ-flows under the name of time-change equivalence, where it is closely connected with the concept of Kakutani equivalence of induced transformations. When viewed from the ergodic theoretical viewpoint, SOE has a rich structure in dimension one, but, as discovered by Rudolph, all ergodic measure-preserving ℝd-flows, d > 1, are SOE. Miller and Rosendal initiated the study of this concept from the point of view of descriptive set theory, where phase spaces of flows aren’t endowed with any measures. This significantly enlarges the class of potential orbit equivalences, and they proved that all nontrivial free Borel ℝ-flows are SOE. They posed a question of whether the same remains to be true in dimension d>1. In this talk, we answer their question in the affirmative, and show that all nontrivial Borel ℝd-flows are SOE.
Information: contact solecki@cornell.edu ahead of time to participate.

May 13

Jerusalem Set Theory Seminar
Time: Wednesday, May 13, 11:00am (Israel Time)
Speaker: Alejandro Poveda (Universitat de Barcelona)
Title: Sigma-Prikry forcings and their iterations (Part II)
Abstract:In the previous talk, we introduced the notion of \Sigma-Prikry forcing and showed that many classical Prikry-type forcing which center on countable cofinalities fall into this framework.
The aim of this talk is to present our iteration scheme for \Sigma-Prikry forcings.
In case time permits, we will also show how to use this general iteration theorem to derive as a corollary the following strengthening of Sharon’s theorem: starting with \omega-many supercompact cardinals one can force a generic extension where Refl(<\omega,\kappa^+) holds and the SCH_\kappa fails, for \kappa being a strong limit cardinal with cofinality \omega
Information: contact omer.bn@mail.huji.ac.il ahead of time in order to participate.

Paris-Lyon Séminaire de Logique
Time:
Wednesday, May 13, 16:00-17:15 CEST
Speaker: Caroline Terry (University of Chicago)
Title: Speeds of hereditary properties and mutual algebricity
Abstract: A 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 distinct elements in H with underlying set {1,…,n}. Not just any function can occur as the speed of hereditary graph property. Specifically, there are discrete “jumps” in the possible speeds. Study of these jumps began with work of Scheinerman and Zito in the 90’s, and culminated in a series 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 hypergraph analogues of many of the jumps from the graph setting, specifically those involving the polynomial, exponential, and factorial speeds. The jumps in the factorial range turned out to have surprising connections to the model theoretic notion of mutual algebricity, which we also discuss.
Information: Join via the link on the seminar webpage 10 minutes before the talk.

Bristol Logic and Set Theory Seminar
Time:
Wednesday, May 13, 14:00-15:30 (UK time)
Speaker: Philip Welch (University of Bristol)
Title: Higher type recursion for infinite time Turing machines III
Abstract:This is part of a series informal working seminars on an extension of Kleene’s early 1960’s on recursion in higher types. (This formed a central theme on the borders of set theory and recursion theory in the 60’s and early 70’s, although now unfortunately not much discussed. Amongst the main names here were Gandy, Aczel, Moschovakis, Harrington, Normann.) We aim to present a coherent version of type-2 recursion for the infinite time Turing machine model. We aim to be somewhat (but not entirely) self-contained. Basic descriptive set theory, and recursion theory, together with admissibility theory will be assumed.

CUNY Set Theory Seminar
Time: Wednesday, May 13, 7pm New York time (1am May 14 CEST)
Speaker: Laurence Kirby, CUNY
Title: Bounded finite set theory
Abstract: There is a well-known close logical connection between PA and finite set theory. Is there a set theory that corresponds in an analogous way to bounded arithmetic IΔ0? I propose a candidate for such a theory, called IΔ0S, and consider the questions: what set-theoretic axioms can it prove? And given a model M of IΔ0 is there a model of IΔ0S whose ordinals are isomorphic to M? The answer is yes if M is a model of Exp; to obtain the answer we use a new way of coding sets by numbers.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

May 14

Kurt Gödel Research Center Seminar (organised by Ben Miller)
Time:
Thursday, May 14, 16:00 CEST
Speaker: Andrew Brooke Taylor, University of Leeds (UK)
Title: Product of CW complexes
Abstract: CW spaces are often presented as the “spaces of choice” in algebraic topology courses, being relatively nice spaces built up by successively gluing on Euclidean balls of increasing dimension. However, the product of CW complexes need not be a CW complex, as shown by Dowker soon after CW complexes were introduced. Work in the 1980s characterised when the product is a CW complex under the assumption of CH, or just b=ℵ1. In this talk I will give and prove a complete characterisation of when the product of CW complexes is a CW complex, valid under ZFC. The characterisation however involves b; the proof is point-set-topological (I won’t assume any knowledge of algebraic topology) and uses Hechler conditions.
Information: Talk via zoom.

May 15

CUNY Set Theory Seminar
Time: Friday, May 15, 2pm New York time (8pm CEST)
Speaker: Ali Enayat, University of Gothenburg
Title: Recursively saturated models of set theory and their close relatives: Part I
Abstract: A model M of set theory is said to be ‘condensable’ if there is an ‘ordinal’ α of M such that the rank initial segment of M determined by α is both isomorphic to M, and an elementary submodel of M for infinitary formulae appearing in the well-founded part of M. Clearly if M is condensable, then M is ill-founded. The work of Barwise and Schlipf in the mid 1970s showed that countable recursively saturated models of ZF are condensable.
In this two-part talk, we present a number of new results related to condensable models, including the following two theorems.
Theorem 1. Assuming that there is a well-founded model of ZFC plus ‘there is an inaccessible cardinal’, there is a condensable model M of ZFC which has the property that every definable element of M is in the well-founded part of M (in particular, M is ω-standard, and therefore not recursively saturated).
Theorem 2. The following are equivalent for an ill-founded model M of ZF of any cardinality:
(a) M is expandable to Gödel-Bernays class theory plus Δ11-Comprehension.
(b) There is a cofinal subset of ‘ordinals’ α of M such that the rank initial segment of M determined by α is an elementary submodel of M for infinitary formulae appearing in the well-founded part of M.
Moreover, if M is a countable ill-founded model of ZFC, then conditions (a) and (b) above are equivalent to:
(c) M is expandable to Gödel-Bernays class theory plus Δ11-Comprehension + Σ12-Choice.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.