For a list of talks in the coming weeks, see https://ests.wordpress.com/online-activities-2021.
Paris-Lyon Séminaire de Logique
Time: Wednesday, 20 January, 16:00-17:00 CEST
Speaker: Gianluca Basso, University of Lyon
Title: Compact metrizable structures via projective Fraïssé theory
Abstract: The goal of projective Fraïssé theory is to approximate compact metrizable spaces via classes of finite structures and glean topological or dynamical properties of a space by relating them to combinatorial features of the associated class of structures. We will discuss general results, using the framework of compact metrizable structures, as well as applications to the study a class of one-dimensional compact metrizable spaces, that of smooth fences, and to a particular smooth fence with remarkable properties, which we call the Fraïssé fence.
Information: Join via the link on the seminar webpage 10 minutes before the talk.
Barcelona Set Theory Seminar
Time: Wednesday, 20 January, 16:00-17:30 CET
Speaker: Vera Fischer, University of Vienna
Title: Independent families in the countable and the uncountable
Abstract: Independent families on w are families of infinite sets of integers with the property that for any two finite subfamilies A and B the set Ç A\È B is infinite. Of particular interest are the sets of the possible cardinalities of maximal independent families, which we refer to as the spectrum of independence. Even though we do have the tools to control the spectrum of independence at w (at least to a large extent), there are many relevant questions regarding higher counterparts of independence in generalised Baire spaces still remaining open.
Information: Online. If you wish to attend, please send an email to bagaria@ub.edu asking for the link.
Bristol Logic and Set Theory Seminar/Oxford Set Theory Seminar
Time: Wednesday, 20 January, 16:00-17:30 UK time (17:00-18:30 CEST)
Speaker: Dima Sinapova, University of Illinois at Chicago
Title: Iteration, reflection, and singular cardinals
Abstract: Two classical results of Magidor are:
(1) from large cardinals it is consistent to have reflection at $\aleph_{\omega+1}$, and
(2) from large cardinals it is consistent to have the failure of SCH at $\aleph_\omega$.These principles are at odds with each other. The former is a compactness type principle. (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 instance of incompactness. The natural question is whether we can have both of these simultaneously. We show the answer is yes.
We describe a Prikry style iteration, and use it to force stationary reflection in the presence of not SCH. Then we obtain this situation at $\aleph_\omega$. This is joint work with Alejandro Poveda and Assaf Rinot.
Information: For the Zoom access code, contact Samuel Adam-Day me@samadamday.com. Link: https://zoom.us/j/96803195711 (open 30 minutes before)
Caltech Logic Seminar
Time: Wednesday, 20 January, 12:00 – 1:00pm Pacific time (21:00 CET)
Speaker: Todor Tsankov, Université Lyon 1
Title: Universal minimal flows of homeomorphism groups of high-dimensional manifolds
Abstract: The first interesting case of a non-trivial, metrizable universal minimal flow (UMF) of a Polish group was computed by Pestov who proved that the UMF of the homeomorphism group of the circle is the circle itself. This naturally led to the question whether a similar result is true for homeomorphism groups of other manifolds (or more general topological spaces). A few years later, Uspenskij proved that the action of a group on its UMF is never 3-transitive, thus giving a negative answer to the question for a vast collection of topological spaces. Still, the question of metrizability of their UMFs remained open and he asked specifically whether the UMF of the homeomorphism group of the Hilbert cube is metrizable. We give a negative answer to this question for the Hilbert cube and all closed manifolds of dimension at least 2, thus showing that metrizability of the UMF of a homeomorphism group is essentially a one-dimensional phenomenon. This is joint work with Yonatan Gutman and Andy Zucker.
Information: See the seminar webpage.
KGRC Research Seminar, Vienna
Time: Thursday, 21 January, 15:00-16:30 CET
Speaker: Juris Steprans, York University, Toronto, Canada
Title: Strong colourings over partitions
Abstract: The celebrated result of Todorcevic that ℵ1↛[ℵ1]2ℵ1 provides a well known example of a strong colouring. A mapping c:[ω1]2→κ is a strong colouring over a partition p:[ω1]2→ω if for every uncountable X⊆ω1 there is n∈ω such that the range of c on [X]2∩p−1{n} is all of κ. I will discuss some recent work with A. Rinot and M. Kojman on negative results concerning strong colourings over partitions and their relation to classical results in this area.
Information: Talk via zoom.
Toronto Set Theory Seminar
Time: Friday, 21 January, 11:00am-12:30pm Toronto time (17:00-18:30 CET)
Speaker: Dima Sinapova, UIC, University of Illinois at Chicago
Title: Iteration, reflection, and singular cardinals
Abstract: Two classical results of Magidor are: (1) from large cardinals it is consistent to have reflection at $\aleph_{\omega+1}$ and (2) from large cardinals it is consistent to have the failure of SCH at $\aleph_{\omega}$.
These principles are at odds with each other. The former is a compactness type principle. (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 instance of incompactness. The natural question is whether we can have both of these simultaneously. We show the answer is yes.
We describe a Prikry style iteration, and use it to force stationary reflection in the presence of not SCH. Then we obtain this situation at $\aleph_{\omega}$ . This is joint work with Alejandro Poveda and Assaf Rinot.
Information: Email Ivan Ongay Valverde ahead of time for the zoom link.
CUNY Set Theory Seminar
Time: Friday, 22 January, 2pm New York time (20:00 CET)
Speaker: Erin Carmody, Fordham University
Title: The relationships between measurable and strongly compact cardinals
Abstract: This talk is about the ongoing investigation of the relationships between measurable and strongly compact cardinals. I will present some of the history of the theorems in this theme, including Magidor’s identity crisis, and give new results. The theorems presented are in particular about the relationships between strongly compact cardinals and measurable cardinals of different Mitchell orders. One of the main theorems is that there is a universe where κ1 and κ2 are the first and second strongly compact cardinals, respectively, and where κ1 is least with Mitchell order 1, and κ2is the least with Mitchell order 2. Another main theorem is that there is a universe where κ1 and κ2are the first and second strongly compact cardinals, respectively, with κ1 the least measurable cardinal such that o(κ1)=2 and κ2 the least measurable cardinal above κ1. This is a joint work in progress with Victoria Gitman and Arthur Apter.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.
Toronto Set Theory Seminar
Time: Friday, 21 January, 1:30-3pm Toronto time (19:30-21:00 CET)
Speaker: Marcos Mazari Armida, Carnegie Mellon University
Title: Universal models in classes of abelian groups and modules
Abstract: The search for universal models began in the early twentieth century when Hausdorff showed that there is a universal linear order of cardinality $\aleph_{n+1}$ if $2^{\aleph_n}= \aleph_{n + 1}$, i.e., a linear order $U$ of cardinality $\aleph_{n+1}$ such that every linear order of cardinality $\aleph_{n+1}$ embeds in $U$. In this talk, we will study universal models in several classes of abelian groups and modules with respect to pure embeddings. In particular, we will present a complete solution below $\aleph_\omega$, with the exception of $\aleph_0$ and $\aleph_1$, to Problem 5.1 in page 181 of \emph{Abelian Groups} by L\'{a}szl\'{o} Fuchs, which asks to find the cardinals $\lambda$ such that there is a universal abelian p-group for purity of cardinality $\lambda$. The solution presented will use both model-theoretic and set-theoretic ideas.
Information: Email Ivan Ongay Valverde ahead of time for the zoom link.
