## 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.

## Asaf Karagila: Spectra of Uniformity

The FG1 Seminar of TU Wien

On Friday Oct 6 at 15:00,  we will meet in the “Dissertantenraum” of the Institute for Discrete Mathematics and Geometry, TU Wien, Wiedner Hauptstr 8-10, 8th floor, green area.

Speaker:  Asaf Karagila

Title: Spectra of Uniformity

Abstract: The existence of uniform ultrafilters on infinite sets is predicated
on the axiom of choice. We discuss some related results, and prove an
Easton-like theorem showing the class of cardinals which carry uniform
ultrafilters has very few provable properties without the axiom of choice.

This is a joint work with Yair Hayut, and can be found on
https://arxiv.org/abs/1709.04824

## Mohammad Golshani: Some properties of Cohen and random reals

Kurt Gödel Research Center – Research Seminar
Thursday, October 5 – 4:00pm in the KGRC lecture room

“Some properties of Cohen and random reals”

(Institute for Research in Fundamental Sciences (IPM), Tehran, Iran)

We discuss some properties of Cohen and random reals. We prove a general combinatorial fact about them which in particular implies that they are large, they contain arbitrary large arithmetical or geometrical progressions, satisfy the Hindman’s conclusion and so on. We also show that they are wild in the sense of o-minimal theory. We also investigate how badly approximable are they by algebraic numbers.

This is a work in progress with Will Brian.

## Abhijit Dasgupta: Axioms for complete elementary extensions

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

Speaker: Abhijit Dasgupta (University of Detroit Mercy)

Title: Axioms for complete elementary extensions

Abstract:

We give an axiomatic framework for “logicless non-standard analysis”, using the notion of partial functions as a primitive.

## Chris Lambie-Hanson: A forcing axiom deciding the generalized Souslin Hypothesis

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

Room:     Wean Hall 8220

Speaker:         Chris Lambie-Hanson
Department of Mathematics
Bar-Ilan University

Title:     A forcing axiom deciding the generalized Souslin Hypothesis

Abstract:

Given a regular, uncountable cardinal $\kappa$, it is often desirable to be able to construct objects of size $\kappa^+$ using approximations of size less than $\kappa$. Historically, such constructions have often been carried out with the help of a $(\kappa,1)$-morass and/or a $\diamondsuit(\kappa)$-sequence.
We present a framework for carrying out such constructions using $\diamondsuit(\kappa)$ and a weakening of Jensen’s $\square_\kappa$. Our framework takes the form of a forcing axiom, $\textrm{SDFA}(\mathcal P_\kappa)$. We show that $\textrm{SDFA}(\mathcal P_κ)$ follows from the conjunction of $\diamondsuit(\kappa)$ and our weakening of $\square_\kappa$ and, if $\kappa$ is the successor of an uncountable cardinal, that $\textrm{SDFA}(\mathcal P_\kappa)$ is in fact equivalent to this conjunction. We also show that, for an infinite cardinal $\lambda$, $\textrm{SDFA}(\mathcal P_{\lambda^+})$ implies the existence of a $\lambda^+$-complete $\lambda^{++}$-Souslin tree. This implies that, if $\lambda$ is an uncountable cardinal, $2^\lambda =\lambda^+$, and Souslin’s Hypothesis holds at $\lambda^{++}$, then $\lambda^{++}$ is a Mahlo cardinal in $L$, improving upon an old result of Shelah and Stanley. This is joint work with Assaf Rinot.

## Osvaldo Guzman Gonzalez: There are no P-points in Silver extensions

Place: Fields Institute (Room 210)

Date: September 29 , 2017 (13:30-15:00)

Speaker: Osvaldo Guzman Gonzalez

Title: There are no P-points in Silver extensions

Abstract: We prove that after adding a Silver real no ultrafilter from the ground
model can be extended to a P-point, and this remains to be the case in any
further extension which has the Sacks property. We use this result to show
that there are no P-points in the Silver model or after adding Silver
reals with the side by side product. In particular, we build models with
no P-points where the continuum can be arbitrarily big. This is joint work
with David Chodounský.

## Boriša Kuzeljević: P-ideal dichotomy and the strong form of the Souslin hypothesis

Dear all,

The seminar meets on Wednesday October 4th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program:
Boriša Kuzeljević — P-ideal dichotomy and the strong form of the
Souslin hypothesis

Best,
David

## Garrett Ervin: The Cube Problem for linear orders II

Mathematical logic seminar – Sep 26 2017
Time:     3:30pm – 4:30 pm

Room:     Wean Hall 8220

Speaker:         Garrett Ervin
Department of Mathematical Sciences
CMU

Title:     The Cube Problem for linear orders II

Abstract:

In the 1950s, Sierpiński asked whether there exists a linear order that is isomorphic to its lexicographically ordered Cartesian cube but not to its square. The analogous question has been answered positively for many different classes of structures, including groups, Boolean algebras, topological spaces, graphs, partial orders, and Banach spaces. However, the answer to Sierpinski’s question turns out to be negative: any linear order that is isomorphic to its cube is already isomorphic to its square, and thus to all of its finite powers. I will present an outline of the proof and give some related results.

## Alejandro Poveda: Woodin’s HOD-Dichotomy

Date: Wednesday 27 September 2017

Time: 16:00

Place: Room S-3
Department of Mathematics & Computer Science
University of Barcelona
Gran Via de les Corts Catalanes 585
08007 Barcelona

Speaker: Alejandro Poveda (Universitat de Barcelona)

Title: Woodin’s HOD-Dichotomy

Abstract: We shall give a complete proof of W. H.
Woodin’s remarkable result that if there exists an
extendible cardinal, then either the set-theoretic universe
V is very “close” to HOD (the class of Hereditarily Ordinal
Definable sets), or it is very “far” from it.