## James Cummings: More on compactness

Mathematical logic seminar – Feb 5 2019
Time:     3:30pm – 4:30 pm

Room:     Wean Hall 8220

Speaker:         James Cummings
Department of Mathematical Sciences
CMU

Title:     More on compactness

Abstract:

I’ll discuss compactness phenomena at regular cardinals, particularly successors of singular cardinals. In particular I’ll explain why ℵω+1 is in some respects completely different from ℵω2+1.

(This talk is related to the talks about compactness that I gave in the Fall semester, but is logically independent)

## Sandra Müller: The consistency strength of long projective determinacy

Tuesday, February 5, 2019, 15.00
Howard House 4th Floor Seminar Room, University of Bristol

Speaker: Sandra Müller (University of Vienna)

Title: The consistency strength of long projective determinacy

Abstract:

We will study infinite two player games and the large cardinal strength corresponding to their determinacy. For games of length $\omega$ this is well understood and there is a tight connection between the determinacy of projective games and the existence of canonical inner models with Woodin cardinals. For games of arbitrary countable length, Itay Neeman proved the determinacy of analytic games of length $\omega \cdot \theta$ for countable $\theta> \omega$ from a sharp for $\theta$ Woodin cardinals.

We aim for a converse at successor ordinals. In joint work with Juan P. Aguilera we showed that determinacy of $\boldsymbol\Pi^1_{n+1}$ games of length $\omega^2$ implies the existence of a premouse with $\omega+n$ Woodin cardinals. This generalizes to a premouse with $\omega+\omega$ Woodin cardinals from the determinacy of games of length $\omega^2$ with $\Game^{\mathbb{R}}\boldsymbol\Pi^1_1$ payoff.

If time allows, we will also sketch how these methods can be adapted to, in combination with results of Nam Trang, obtain $\omega^\alpha+n$ Woodin cardinals for countable ordinals $\alpha$ and natural numbers $n$ from the determinacy of sufficiently long projective games.

Bristol Logic Seminars: https://www.bristolmathsresearch.org/events/logic-and-set-theory/

## Alessandro Vignati: Uniform Roe coronas

Seminar: Working group in applications of set theory, IMPAN

(joint meeting with the Geometric Group Theory Seminar, IMPAN)

Thursday, 7.02.2019, 10:15, room 403, IMPAN

NOTE ROOM CHANGE TO 403

Speaker: Alessandro Vignati (KU Leuven)

Title: “Uniform Roe coronas”

Abstact: “Given a metric space (X,d), one defines a subalgebra of the space of operators on l_2(X) called the uniform Roe algebra of (X,d), denoted C_u*(X). This is the closure of the algebra of finite-propagation operators. The study of these algebras comes from the fact that C_u*(X) catches algebraically some of the large scale geometrical properties of X. Uniform Roe algebras have therefore an intrinsic relation with coarse geometry and the coarse Baum-Connes conjecture.

In recent year, much work was dedicated to show which geometric properties are preserved by isomorphisms of Uniform Roe algebras. Namely, if C_u*(X) and C_u*(Y) are isomorphic, how much do X and Y look alike? We pose the same question for Uniform Roe corona algebras.

Since Cu*(X) contains all compact operators, we can define the natural quotient Q_u*(X)=C_u*(X)/K(l_2(X)), the Uniform Roe corona algebra of X. Which geometric properties do the spaces X and Y share, when an isomorphism between Q_u*(X) and Q_u*(Y) is given? For example, must X and Y be coarsely equivalent, or even bijectively coarsely equivalent? (Two spaces are coarsely equivalent if “they look the same when the observer is far from them”).

We answer these questions with the aid of some set theory, in particular of Forcing Axioms. Forcing Axioms are generalizations of the Baire category theorem. They are alternative to the Continuum Hypothesis, and they’re at the base of many rigidity phenomena observed in the theory of quotients (both discrete such as Boolean algebra quotient, and continuous, as the Calkin algebra or corona C*-algebras). The talk starts with introducing the objects in play. The goal is to state the main results, and at least sketch the salient points of their proofs. We conclude with a list of open questions. This is joint work with Bruno Braga and Ilijas Farah”.

This is the last meeting during the first semester of 2018/19.

Visit our seminar page which may include information on some future talks at https://www.impan.pl/~set_theory/Seminar/

## Moritz Müller: Forcing against bounded arithmetic

BARCELONA RESEARCH GROUP IN SET THEORY

BARCELONA SET THEORY SEMINAR

Forcing against bounded arithmetic

Moritz Müller

Universitat Politècnica de Catalunya

Abstract: We study the following problem. Given a nonstandard
model of arithmetic we want to expand it by a binary relation that
does something prohibitive, e.g. violates the pigeonhole principle in
the sense that it is the graph of a bijection from n+1 onto n for
some (nonstandard) n in the model. The goal is to do so while
preserving as much as possible of true arithmetic. More precisely,
we want the expansion to model the least number principle for a
class of formulas as large as possible. The problem is of central
importance in bounded arithmetic and propositional proof
complexity. It is not well understood. The talk describes a general
method of forcing to produce such expansions.

Date: Thursday 7 February 2019
Time: 16:00

Place: Room S-1*
Departament de Matemàtiques i Informàtica
Universitat de Barcelona
Gran Via de les Corts Catalanes 585, 08007 Barcelona

* Enter the University building through the door 20 meters to the right of the
main door and, as you enter the courtyard, turn left, go to the end of the
corridor, and then downstairs.

## Piotr Szewczak: Selection Principles in Mathematics (an overview)

BIU Infinite Combinatorics Seminar

Piotr Szewczak, Cardinal Stefan Wyszyński University in Warsaw, Poland
04/02/2019 – 13:0015:00

The theory of selection principles deals with the possibility of obtaining mathematically significant objects by selecting elements from sequences of sets. The studied properties mainly include covering properties, measure- and category-theoretic properties, and local properties in topological spaces, especially functions spaces. Often, the characterization of a mathematical property using a selection principle is a nontrivial task leading to new insights on the characterized property.
I will give an overview of this theory and, if time permits, I will present some results obtained jointly with Boaz Tsaban and Lyubomyr Zdomskyy.

# Berkeley conference on inner model theory

## July 08–19, 2019

Organizers: Ralf Schindler (Münster) and John Steel (Berkeley).
This conference will be a sequel to the 1st Conference on the core model induction and hod mice that was held in Münster (FRG), July 19 — August 06, 2010, to the 2nd Conference on the core model induction and hod mice that was held in Münster (FRG), August 08 — 19, 2011, to the AIM Workshop on Descriptive Inner Model Theory, held in Palo Alto (CA), June 02 — 06, 2014, to the Conference on Descriptive Inner Model Theory, held in Berkeley (CA) June 09 — 13, 2014 to the 3rd Münster Conference on inner model theory, the core model induction, and hod mice that was held in Münster (FRG), July 20 — 31, 2015, to the 1st Irvine conference on descriptive inner model theory and hod mice that was held in Irvine (CA), July 18 — 29, 2016, to the 4th Münster Conference on inner model theory, the core model induction, and hod mice that was held in Münster (FRG), July 17 — August 01, 2017, as well as to the 1st Girona conference on inner model theory that was held in Girona (Catalonia), July 16 — 27, 2018.

Once more, this conference will now draw together researchers and advanced students with an interest in inner model theory, in order to communicate and further explore recent work. There will be courses and single talks.
We will meet Monday–Friday, with 2 1/2 hours of lectures in the morning and 2 1/2 hours of lectures in the afternoon. This will leave ample time for problem sessions, informal seminars, and other interactions.

## Logic Fest in the Windy City, Chicago, May 30 – June 2, 2019

The conference will take place at the University of Illinois at Chicago on May 30 – June 2. We will cover topics in set theory, descriptive set theory, model theory, and various applications. The workshop is aimed at graduate students and postdocs, but can also be beneficial to anyone interested in current developments in logic. We will have three tutorials and several talks. The invited speakers are:

Tutorials:

Talks:

Travel support is available. Requests should be directed to Dima Sinapova. Graduate students, young researchers, female mathematicians and members of underrepresented groups are particularly encouraged to apply. Schedule of talks.
Lodging:

## Jordi Lopez Abad: Amalgamation and Ramsey properties of $\ell_p^n$’s

The seminar meets again on Wednesday February 6th at 11:00 in the
Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front
building.

Program: Jordi Lopez Abad — Amalgamation and Ramsey properties of
$\ell_p^n$’s

We will give a proof of the fact that $\{\ell_p^n\}$ have the
approximate Ramsey property and a strong form of amalgamation (they are
Fraïssé classes, in a metric sense). The proofs are divided into 3
cases: $p=\infty$, $p=2$ and $p\neq 2,\infty$. We will also discuss the
case of the families of all finite dimensional subspaces of $L_p(0,1)$
for $p\neq 2,\infty$ and of $C[0,1]$.

## Feng Qi: On investigation of some foundational problems of economics

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 30 January 2019, 17:00 hrs

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

Speaker: Feng Qi

Title: On investigation of some foundational problems of economics

Abstract: I shall present some of my toughts regarding some foundational
problems of economics from mathematical logic point of view.

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

## Arturo Martínez-Celis: Porous sets on the Cantor set

Seminar: Working group in applications of set theory, IMPAN

Thursday, 31.01.2019, 10:15, room 105, IMPAN

Speaker: Arturo Martínez-Celis (IM PAN)

Title: “Porous sets on the Cantor set”

Abstact: “Given a completely metrizable space X, a subset A of X is a strongly porous set if there is a positive constant p such that for any open ball B of radius r smaller than 1, there is an open ball B’ inside of B of radius rp such that B’ evades the set A. We will study the cardinal invariants related to the σ-ideal generated by strongly porous sets on the Cantor space and its relation with other known σ-ideals of the real line. We will also uncover a deep connection between the σ-ideal of the strongly porous sets and some instances of the Martin’s Axiom. “.

Visit our seminar page which may include information on some future talks at https://www.impan.pl/~set_theory/Seminar/