# Category Archives: Seminars

## Andres Caicedo: Real-valued measurability and the extent of Lebesgue measure

Thursday, November 9, 2017, from 4 to 5:30pm
East Hall, room 3096

Speaker: Andres Caicedo (Math Reviews)

Title: Real-valued measurability and the extent of Lebesgue measure

Abstract:

The existence of an atomlessly measurable cardinal is equivalent to the existence of a measure extending Lebesgue measure and defined on all sets of reals. I’ll start the talk with some background on real-valued measurability, and proceed to argue that the assumption that there is some such cardinal actually has an effect on the extent of Lebesgue measure itself. The result goes beyond what can be granted arguing merely in terms of consistency strength.

## Francisco Guevara Parra: Finite products of M-separeble spaces

Place: Fields Institute (Room 210)

Date: November 3, 2017 (13:30-15:00)

Speaker: Francisco Guevara Parra

Title: Finite products of M-separeble spaces

Abstract: A topological space is called M-separable if for all sequence of dense sets, we can select a finite subset from each dense set so that the union of those finite sets is dense. We will study the finite productivity of this property when we assume the spaces are countable and sequential.

## Chris Lambie-Hanson: Squares, ascent paths, and chain conditions

BIU seminar in Set Theory

On 06/11/2017, 13-15, Building 505, Room 65

Speaker: Chris Lambie-Hanson

Title: Squares, ascent paths, and chain conditions

Abstract. Two topics of interest in modern set theory are the productivity of chain conditions and the existence of higher Aronszajn trees. In this talk, we discuss generalizations of both of these topics and their connections with various square principles. In particular, we will prove that, if $\kappa$ is a regular uncountable cardinal and $\square(\kappa)$ holds, then:
1) for all regular $\lambda < \kappa$, there is a $\kappa$-Aronszajn tree with a $\lambda$-ascent path;
2) there is a $\kappa$-Knaster poset $\mathbb{P}$ such that $\mathbb{P}^{\aleph_0}$ is not $\kappa$-c.c.
Time permitting, we will also present a complete picture of the relationship between the existence of special trees and the existence of Aronszajn trees with ascent paths at the successor of a regular cardinal. This is joint work with Philipp Lücke.

## Barnabas Farkas: Cardinal invariants versus towers in analytic P-ideals / An application of matrix iteration

Tuesday, November 7, 2017, 17:15
Wrocław University of Technology, 215 D-1

Speaker: Barnabas Farkas (TU Wien)

Title: Cardinal invariants versus towers in analytic P-ideals / An application of matrix iteration

Abstract:

I will present two models concerning interactions between the existence of towers in analytic P-ideals and their cardinal invariants. It is trivial to see that if there is no tower in $\mathcal{I}$, then $\mathrm{add}^*(\mathcal{I})<\mathrm{cov}^*(\mathcal{I})$. I will prove that this implication cannot be reversed no matter the value of $\mathrm{non}^*(\mathcal{I})$. More precisely, let $\mathcal{I}$ be an arbitrary tall analytic P-ideal, I will construct the following two models:

Model1 of $\mathrm{non}^*(\mathcal{I})=\mathfrak{c}$,
there is a tower in $\mathcal{I}$, and $\mathrm{add}^*(\mathcal{I})<\mathrm{cov}^*(\mathcal{I})$. Method: Small filter iteration.

Model2 of $\mathrm{non}^*(\mathcal{I})<\mathfrak{c}$,
there is a tower in $\mathcal{I}$, and $\mathrm{add}^*(\mathcal{I})<\mathrm{cov}^*(\mathcal{I})$. Method: Matrix iteration.

This is a joint work with J. Brendle and J. Verner.

## Clinton Conley: Measure-theoretic unfriendly colorings

Mathematical logic seminar – Oct 31 2017
Time:     3:30pm – 4:30 pm

Room:     Wean Hall 8220

Speaker:         Clinton Conley
Department of Mathematical Sciences
CMU

Title:     Measure-theoretic unfriendly colorings

Abstract:

Given a graph with vertices painted red and blue, we say the coloring is unfriendly if every red vertex has at least as many blue neighbors as red, and vice versa. Every finite graph admits an unfriendly coloring, but (ridiculously) it remains open whether every countable graph does. Rather than tackle that problem, we consider measure-theoretic analogs associated with probability-measure-preserving actions of finitely generated groups. We don’t really answer any questions here, either, but we do obtain such colorings up to weak equivalence of actions. Time permitting, we also discuss recent constructions of unfriendly colorings of acyclic hyperfinite graphs. The talk may include joint work with Kechris, Marks, Tucker-Drob, and Unger.

## Danny Nguyen: Presburger Arithmetic and its computational complexity

Thursday, November 2, 2017, from 4 to 5:30pm
East Hall, room 3096

Speaker: Danny Nguyen (University of California, Los Angeles)

Title: Presburger Arithmetic and its computational complexity

Abstract:

Presburger Arithmetic (PA) is a classical topic in logic, with numerous connections to computer science and combinatorics. Formally, is the first order structure on the integers with only additions and inequalities. Despite its long history, many problems in PA have remained unsolved until recently. We study the complexity of decision problems in PA, and classify them according to hierarchy levels. Along the way, connections to Integer Programming and Optimization will be explained. The talk will be self contained and assumes no prior knowledge of the subject. Joint work with Igor Pak.

## Yair Hayut: Magidor cardinal and Magidor filters

BIU seminar in Set Theory

On 30/10/2017, 13-15, Building 505, Room 65

Speaker: Yair Hayut (TAU)

Title: Magidor cardinal and Magidor filters

Abstract. In this talk I will define the notion of Magidor Cardinal (\omega bounded Jonsson cardinal) which is a generalization of Jonsson cardinal.
I will show that the analog of Jonsson filter for Magidor cardinals
is inconsistent with ZFC.

This lecture is based on a joint work with Shimon Garti and Saharon Shelah.

## Ralf Schindler: A Hamel basis for the reals without choice

BARCELONA SET THEORY SEMINAR

Date: Monday 30 October 2017

Time: 16:00

Place: IMUB*
University of Barcelona
Gran Via de les Corts Catalanes 585
08007 Barcelona

Speaker: Ralf Schindler

Title: A Hamel basis for the reals without choice (Universität Münster)

Abstract: The Cohen-Halpern-Levy model N has an infinite set of
reals without a countable subset. Answering a question of D.
Pincus and K. Prikry from 1975, we show that there is a Hamel
basis (i.e., a basis for R as a vector space over Q) in N. This is
joint work with Liuzhen Wu and Liang Yu, inspired by earlier joint
work with Mariam Beriashvili. The axiom of Dependent Choice
(DC) fails in N, but in later joint work with Wu and Yu we also
showed that there is a model of ZF+DC with a Hamel basis and in
which the reals cannot be wellordered.

## Haim Horowitz: Martin’s Maximum and the saturation of the nonstationary ideal

Place: Fields Institute (Room 210)

Date: October 27, 2017 (13:30-15:00)

Speaker: Haim Horowitz

Title: Martin’s Maximum and the saturation of the nonstationary ideal

Abstract:

By a classical result of Foreman, Magidor and Shelah, MM implies that the nonstationary ideal on $\omega_1$ is $\aleph_2$-saturated. We shall prove that MM actually implies a stronger saturation property for the nonstationary ideal. As a corollary, we obtain a new proof of the fact that the continuum is $\aleph_2$ under MM.

This is joint work with Shimon Garti and Menachem Magidor

## Egbert Thümmel and Boriša Kuzeljević: the P-ideal dichotomy

Dear all,

The seminar meets on Wednesday November 1st at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program: Egbert Thümmel and Boriša Kuzeljević will review some classical
as well as new facts and applications of the P-ideal dichotomy (PID).

Best,
David