## Andy Zucker: Maximal equivariant compactifications of categorical metric structures

Mathematical logic seminar – Mar 27 2018
Time:     3:30pm – 4:30 pm

Room:     Wean Hall 8220

Speaker:         Andy Zucker
Department of Mathematical Sciences
CMU

Title:     Maximal equivariant compactifications of categorical metric structures

Abstract:

Any completely regular space embeds into a compact space. But suppose G is a topological group and X is a completely regular G-space. There is a largest G-map αX: X → Y where Y is compact and αX has dense image, but αX need not be an embedding. Recently, Pestov has constructed an example of a topological group G and non-trivial flow X for which αX is the map to a singleton.

In this talk, we consider automorphism groups of categorical metric structures, which include the Urysohn sphere, the unit sphere of the Banach lattice Lp, and the unit sphere of the Hilbert space L2. We show that if G is the group of automorphisms of a categorical metric structure X, then αX is the embedding of X into the space of 1-types over X.

(Joint work with Itai Ben Yaacov)

## Antonio Aviles: Free Banach lattices

Place: Fields Institute (Room 210)

Date: March 23, 2018 (14:05-15:05)

Speaker: Antonio Aviles

Title: Free Banach lattices

Abstract: A Banach lattice has compatible structures of both Banach space and lattice. In this talk we present free constructions of Banach lattices based on a given Banach space or based on a given lattice, and we discuss some of their properties, like chain conditions ccc and others.

## Slawomir Solecki: Polishable equivalence relations

Place: Fields Institute (Room 210)

Date: March 23, 2018 (13:00-14:00)

Speaker: Slawomir Solecki

Title: Polishable equivalence relations

Abstract: We introduce the notion of Polishable equivalence relations. This class of equivalence relations contains all orbit equivalence relations induced by Polish group actions and is contained in the class of idealistic equivalence relations of Kechris and Louveau. We show that each orbit equivalence relation induced by a Polish group action admits a canonical transfinite sequence of Polishable equivalence relations approximating it. The proof involves establishing a lemma, which may be of independent interest, on stabilization of increasing ω1-sequences of completely metrizable topologies.

## Takeuti Memorial Symposium, Kobe, September 18 – 20, 2018

AML 2018 – Takeuti Memorial Symposium

Symposium on Advances in Mathematical Logic 2018

Dedicated to the Memory of Professor Gaisi Takeuti (1926-2017)

September 18 (Tue) – 20 (Thu), 2018

Kobe, Japan

• Scope

Mathematical logic and related areas including, not restricted to,
proof theory, set theory, computability theory, model theory, philosophical logic,
theoretical computer science, philosophy of mathematics.

• Venue

Takigawa Memorial Hall, Rokkodai Campus, Kobe University
1-1 Rokkodai, Nada, Kobe 657-8501, Japan

• Invited Speakers

Samuel R. Buss (San Diego)
Wilfried Sieg (CMU)
(Other invited speakers will be announced later.)

• Proceedings Volume

A proceedings volume of selected and revised papers will be published after the symposium.

• Important Dates (tentative)

Deadline of abstracts for contributed talk: July, 2018

Symposium: September 18-20, 2018
Deadline of full papers for the proceedings volume: March, 2019
Publication of the proceedings volume: December 2019

• Previous Related Event

Symposium on Mathematical Logic 2003 (Takeuti Symposium)

• Organizers

Toshiyasu Arai (Chiba)
Makoto Kikuchi (Kobe)
Satoru Kuroda (Gunma Prefectural Women’s University)
Teruyuki Yorioka (Shizuoka)

KAKENHI: JSPS Grant-in-Aid for Scientific Research
Japan Association for Philosophy of Science

• Contact

Makoto Kikuchi (mkikuchi@kobe-u.ac.jp)

## Monroe Eskew: Local saturation of the nonstationary ideals

Talk held by Monroe Eskew (KGRC) at the KGRC seminar on 2018-03-22.

Abstract: It is consistent relative to a huge cardinal that for all successor cardinals $\kappa$, there is a stationary $S \subseteq \kappa$ such that the nonstationary ideal on $\kappa$ restricted to $S$ is $\kappa^+$-saturated. We will describe the construction of the model, focusing how to get this property on all $\aleph_n$ simultaneously. Time permitting, we will also briefly discuss the Prikry-type forcing that extends this up to $\aleph_{\omega+1}$.

## Grzegorz Plebanek: Strictly positive measures on Boolean algebras

Tuesday, March 27, 2018, 17:15
Wrocław University of Technology, 215 D-1

Speaker: Grzegorz Plebanek (University of Wroclaw)

Title: Strictly positive measures on Boolean algebras

Abstract:

$SPM$ denotes the class of Boolean algebras possessing strictly positive measure (finitely additive and probabilistic). Together with Menachem Magidor, we consider the following problem: Assume that $B$ belongs to $SPM$ for every subalgebra $B$ of a given algebra $A$ such that $|B|\le\mathfrak c$. Does it imply that the algebra $A$ belongs to $SPM$?

It turns out that the positive answer follows from the existence of some large cardinals, while the counterexample can be found in the model of $V=L$.

## David Chodounsky: How to kill a P-point

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 14 March 2018, 17:00 hrs

Room: S17#04-06, Department of Mathematics, NUS

Speaker: David Chodounsky

Title: How to kill a P-point

URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html

Abstract:
The existence of P-points (also called P-ultrafilters) is independent
of the axioms of set theory ZFC. I will present the basic ideas behind
a new and simple proof of the negative direction of this fact; a new
forcing method for destroying P-points.

## Thilo Weinert: Cardinal Characteristics and Partition Properties

Talk held by Thilo Weinert (KGRC) at the KGRC seminar on 2018-03-15.

Abstract: Many a partition relation has been proved assuming the Generalised Continuum Hypothesis. More precisely, many negative partition relations involving ordinals smaller than $\omega_2$ have been proved assuming the Continuum Hypothesis. Some recent results in this vein for polarised partition relations came from Garti and Shelah. The talk will focus on classical partition relations. The relations $\omega_1\omega \not\rightarrow (\omega_1\omega, 3)^2$ and $\omega_1^2 \not\rightarrow (\omega_1\omega, 4)^2$ were both shown to follow from the Continuum Hypothesis, the former in 1971 by Erdős and Hajnal and the latter in 1987 by Baumgartner and Hajnal.

The former relation was shown to follow from both the dominating number and the stick number being $\aleph_1$ in 1987 by Takahashi. In 1998 Jean Larson showed that simply the dominating number being $\aleph_1$ suffices for this. It turns out that the unbounding number and the stick number both being $\aleph_1$ yields the same result. Moreover, also the second relation follows both from the dominating number being  $\aleph_1$ and from both the unbounding number and the stick number being $\aleph_1$ thus answering a question of Jean Larson.

This is both joint work with Chris Lambie-Hanson and with both William Chen and Shimon Garti.

## David J. Fernández Bretón: Models of set theory with union ultrafilters and small covering of meagre, II

Thursday, March 15, 2018, from 4 to 5:30pm
East Hall, room 3088

Speaker: David J. Fernández Bretón (University of Michigan)

Title: Models of set theory with union ultrafilters and small covering of meagre, II

Abstract:

Union ultrafilters are ultrafilters that arise naturally from Hindman’s finite unions theorem, in much the same way that selective ultrafilters arise from Ramsey’s theorem, and they are very important objects from the perspective of algebra in the Cech–Stone compactification. The existence of union ultrafilters is known to be independent from the ZFC axioms (due to Hindman and Blass–Hindman), and is known to follow from a number of set-theoretic hypothesis, of which the weakest one is that the covering of meagre equals the continuum (this is due to Eisworth). In the first part of this two-talk series I exhibited a model of ZFC with union ultrafilters whose covering of meagre is strictly less than the continuum, obtained by means of a short countable support iteration. In this second talk, I will exhibit two more such models, one obtained by means of a countable support iteration of proper forcings, and the other by means of a single-step forcing (modulo being able to obtain an appropriate ground model).

## Yasser Fermán Ortiz Castillo: Crowded pseudocompact spaces of cellularity at most the continuum are resolvable

Place: Fields Institute (Room 210)

Date: March 9 , 2018 (13:30-15:00)

Speaker: Yasser Fermán Ortiz Castillo

Title: Crowded pseudocompact spaces of cellularity at most the continuum are resolvable

Abstract: It is an open question from W. Comfort and S. Garcia-Ferreira if it is true that every crowded pseudocompact space is resolvable. In this talk will be present a partial positive answer for spaces of cellularity at most the continuum.