Category Archives: Seminars

Jan Grebik: Borel selectors of Borel ideals (continued)

Dear all,

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

Program: Jan Grebik — Borel selectors of Borel ideals (continued)
We present a result that there is an F_sigma ideal without Borel
selector and deduce that Galvin’s lemma does not have a “Borel proof.”
We also show that Nash-Williams theorem has a “Borel proof” and
therefore Galvin’s lemma is intrinsically more complex than
Nash-Williams theorem.

Best,
David

Monroe Eskew: Global Chang’s Conjecture

KGRC Research seminar on 2017-10-19 at 4pm.

Speaker: Monroe Eskew (KGRC)

Abstract: Instances of Chang’s Conjecture (CC) can be seen as a generalization of the Loweheim-Skolem Theorem to a logic in between those the first and second order. Foreman asked how far the analogy with Lowenheim-Skolem can go, specifically whether a global version of CC is consistent. In joint work with Yair Hayut, the speaker answered Foreman’s question affirmatively, and in the process lowered the known upper bounds on consistency strength for many instances of CC. We will discuss the results, as well as some barriers that singular cardinal combinatorics impose on the possibility of a stronger global CC.

Vahagn Aslanyan: Schanuel’s conjecture, pseudo-exponentiation, and Ax’s theorem

Mathematical logic seminar – Oct 17 2017

Time:     3:30pm – 4:30 pm

Room:     Wean Hall 8220

Speaker:         Vahagn Aslanyan
Department of Mathematical Sciences
CMU

Title:     Schanuel’s conjecture, pseudo-exponentiation, and Ax’s theorem

Abstract:

Schanuel’s conjecture captures the transcendence properties of the complex exponential function, and is considered out of reach. An interesting, novel approach to it was given by Zilber which led to the construction of pseudo-exponentiation. This gave rise to more conjectures related to Schanuel’s conjecture and the complex exponential field C_exp. One of those, known as Zilber-Pink, is purely number theoretic and generalises many known conjectures (and results) in diophantine geometry such as Mordell-Lang and Andree-Oort. I will describe Zilber’s construction and the Zilber-Pink conjecture. If time permits, I will also discuss a functional analogue of Schanuel’s conjecture proven by Ax in 1971.

Jan Grebik: Borel selectors of Borel ideals

Dear all,

The seminar meets on Wednesday October 18th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program: Jan Grebik — Borel selectors of Borel ideals
We present a result that there is an F_sigma ideal without Borel
selector and deduce that Galvin’s lemma does not have a “Borel proof.”
We also show that Nash-Williams theorem has a “Borel proof” and
therefore Galvin’s lemma is intrinsically more complex than
Nash-Williams theorem.

Best,
David

Frank Tall: Completely Baire spaces, Menger spaces, projective sets, Hurewicz’ theorems, and an application to Model Theory

Place: Fields Institute (Room 210)

Date: October 13, 2017 (13:30-15:00)

Speaker: Frank Tall

Title:Completely Baire spaces, Menger spaces, projective sets, Hurewicz’ theorems,  and an application to Model Theory

Abstract: We prove the following are equiconsistent:
(1) There is an inaccessible cardinal.
(2) Every projective Menger set of reals is σ-compact.
(2’) Every co-analytic Menger set of reals is σ-compact.
(3) Every projective set of reals with every closed subset Baire is Polish.
(3’) Every analytic set of reals with every closed subset Baire is Polish.
(1), (2), (2’) are from Tall-Todorcevic-Tokg ̈z 2017; (1), (3), (3’) are from Tall-Zdomskyy, in preparation.

Researchers previously derived (2), (3) from the Axiom of Projective Determinacy, and negations of (2’) and (3’) from V = L. We substitute a perfect set version of Todorcevic’s Open Graph Axiom for PD and the L[a] existence of an a ⊆ ω such that $\omega_1=\omega_1$ for V = L.

We (Tall-Zdomskyy) also construct in ZFC a separable metric space X such that every closed subset of X ω is Baire, but X includes no dense completely metrizable subspace. Such a space was previously constructed by Eagle-Tall (2017) from a non-meager P-filter, which is not known to exist in ZFC. Such a space can be used to construct an abstract logic in which the Omitting Types Theorem holds but a stronger, game-theoretic version of the OTT does not.

Ziemowit Kostana: Non-measurability of algebraic sum

Sunday, September 17, 2017, 17:15
Wrocław University of Technology, 215 D-1

Speaker: Ziemowit Kostana (University of Warsaw)

Title: Non-measurability of algebraic sum

Abstract:

Consider following problems:
1. If A is meagre (null) subset of real line, does there necessarily exist set B such that algebraic sum A+B doesn’t have Baire property (is non-measurable)?
2. If A is meagre (null) subset of real line, does there necessarily exist non-meagre (non-null) additive subgroup, disjoint with some translation of A?

It is not hard to prove that positive answer to 2. implies positive answer to 1, both for measure and category.
We answer 2. affirmatively for category, while version for measure turns out to be independent of ZFC. The latter was essentially proved last year
by A. Rosłanowski and S. Shelah. Both results holds for Cantor space with coordinatewise addition mod. 2 as well.

Gao Ziyuan: Erasing pattern languages distinguishable by a finite number of strings

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 11 October 2017, 17:00 hrs

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

Speaker: Gao Ziyuan

Title: Erasing pattern languages distinguishable by a finite number of strings

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

Abstract:
Pattern languages have been an object of study in various subfields of
computer science for decades. We introduce and study a decision
problem on patterns called the finite distinguishability problem:
given a pattern pi, are there finite sets T+ and T- of
strings such that the only pattern language containing all strings in
T+ and none of the strings in T- is the language generated by
pi? This problem is related to the complexity of teacher-directed
learning, as studied in computational learning theory, as well as to
the long-standing open question whether the equivalence of two
patterns is decidable. We show that finite distinguishability is
decidable if the underlying alphabet is of size other than 2 or 3, and
provide a number of related results, such as (i) partial solutions for
alphabet sizes 2 and 3, and (ii) decidability proofs for variants of
the problem for special subclasses of patterns, namely, regular,
1-variable, and non-cross patterns. For the same subclasses, we
further determine the values of two complexity parameters in
teacher-directed learning, namely the teaching dimension and the
recursive teaching dimension.

Aleksander Cieślak: Ideals of subsets of plane

Sunday, September 10, 2017, 17:15
Wrocław University of Technology, 215 D-1

Speaker: Aleksander Cieślak (Wrocław University of Technology)

Title: Ideals of subsets of plane

Abstract:

For given two ideals $I$ and $J$ of subsets of Polish space $X$ we define a Fubini product $I\times J$ as all these subsets of plane $X^2$ which can be covered by a Borel set $B$ such that $I$-almost all its vertical sections are $J$-small. We will investigate how properties of factors influence properties of product.

Saeed Ghasemi: Isomorphisms between reduced

Dear all,

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

Program: Saeed Ghasemi — Isomorphisms between reduced
products of matrices

The talk will be mostly based on the paper:
https://arxiv.org/abs/1310.1353

Best,
David

David J. Fernández Bretón: Higher degree versions of the Central Sets Theorem

Thursday, October 12, 2017, from 4 to 5:30pm
East Hall, room 3096

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

Title: Higher degree versions of the Central Sets Theorem

Abstract:

The Central Sets Theorem is a Ramsey-theoretic result due to Furstenberg, from 1981, and multiple generalizations of it (in a variety of different directions) have been proved afterwards (to the best of my knowledge, the currently most general statement is due to De, Hindman and Strauss in 2008, but there are also many relevant results due to Bergelson). In this series of two talks, we will explain how to interpret the Central Sets Theorem as a statement about linear polynomials in a polynomial ring with countably many variables, and prove a couple of natural generalizations involving polynomials of higher degree. In order to make this exposition self-contained, we will spend most of the first talk providing an overview of the techniques from algebra in the Cech–Stone compactification, which is the main tool that we use in our proof.