## Osvaldo Guzman Gonzalez: The Shelah-Steprans property of ideals

Place: Fields Institute (Room 210)

Date: November 17, 2017 (13:30-15:00)

Speaker: Osvaldo Guzman Gonzalez

Title: The Shelah-Steprans property of ideals

Abstract: An ideal I has the Shelah-Steprans property if for every set X of finite sets, there is an element of I that either intersects every element of X or contains infinitely many elements of X. We will give a characterization of the Borel Shelah-Steprans ideals in terms of the Katetov order and we will see some applications in the destructibility of MAD families.

## Eilon Bilinsky: Uncountable set of reals with a single accumulation point

BIU seminar in Set Theory

On 20/11/2017, 13-15, Building 505, Room 65

Speaker: Eilon Bilinsky (TAU)

Title: Uncountable set of reals with a single accumulation point

Abstract. We construct a model of ZF with an uncountable set of reals having a unique condensation point. This answers a question of Sierpinski from 1918.

## 11th Young Set Theory Workshop, Lausanne, June 25–29, 2018

The aims of the Young Set Theory workshops are to bring together young researchers in the domain of set theory and give them the opportunity to learn from each other and from experts in a friendly environment. A long-term objective of this series of workshops is to create and maintain a network of young set theorists and senior researchers, so as to establish working contacts and help disseminate knowledge in the field.

This year’s Young Set Theory Workshop will take place at the Bernoulli Center in Lausanne, Switzerland, at the end of the Descpriptive set theory and Polish groups semester. While the organization of the workshop is independent of that of the semester, we hope the proximity will promote attendance of young researchers from extra-European countries.

### Tutorial Speakers

• Ilijas Farah (York University)
• Assaf Rinot (Bar-Ilan University)
• Christian Rosendal (University of Illinois at Chicago)
• Dima Sinapova (University of Illinois at Chicago)

### Invited Speakers

• Hazel Brickhill (University of Kobe)
• Diana Montoya (Kurt Gödel Research Center)
• Gianluca Paolini (Hebrew University of Jerusalem)
• Yann Pequignot (University of California, Los Angeles)

### Invited LOCAL Speakers

• Lorenz Halbeisen (ETH Zürich)
• Gerhard Jäger (University of Bern)

## Paul Ellis – Cycle Reversions and Dichromatic Number in (Infinite) Tournaments

KGRC seminar on 2017-11-16 at 3:30pm

Speaker: Paul Ellis (Manhattanville College, New York, USA)

Abstract: The dichomatic number for a digraph is the least number of acyclic subgraphs needed to cover the graph. In 2005, Pierre Charbit showed that by iterating the operation {select a directed cycle, and reverse the direction of each arc in it} that the dichromatic number in any finite digraph can be lowered to 2. This is optimal, as a single directed cycle will always have dichromatic number 2. Recently, Daniel Soukup and I showed that the same is true for infinite tournaments of any cardinality, and in fact, we proved this by induction. Along the way to proving this, we uncovered some nice structural facts about infinite digraphs that we think are of more general interest. While this talk will be mostly graph theoretic in flavor, we did need to put on our set theory glasses to distinguish between the singular and regular cases in the induction. I should note that the question remains open for arbitrary inifinite digraphs, even those of countable cardinality.

## Clinton Conley: Measure-theoretic unfriendly colorings II

Mathematical logic seminar – Nov 14 2017
Time:     3:30pm – 4:30 pmRoom:     Wean Hall 8220

Speaker:         Clinton Conley
Department of Mathematical Sciences
CMU

Title:     Measure-theoretic unfriendly colorings II

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.

## Philipp Lücke: Squares, chain conditions, and products

Monday, November 13, 2017, 16.30
Seminar room 0.008, Mathematical Institute, University of Bonn

Speaker: Philipp Lücke (Universität Bonn)

Title: Squares, chain conditions, and products

Abstract:

With the help of square principles, we obtain results concerning the consistency strength of several statements about strong chain conditions and their productivity. In particular, we show that if the κ-Knaster property is countably productive for some uncountable regular cardinal κ, then κ is weakly compact in L. The proof of this result relies on a new construction that shows that Todorcevic’s principle □(κ) implies an indexed version of the principle □(κ,λ). This is joint work with Chris Lambie-Hanson (Bar-Ilan).

## Logic Colloquium 2018, Udine, July 23 – 28, 2018

The Logic Col­lo­quium 2018 is the an­nual Eu­ro­pean summer meeting of the As­so­ci­a­tion of Sym­bolic Logic (ASL), that will be held during July 23—28, 2018 at the Uni­ver­sity of Udine, Italy.

# Com­mit­tees

## Šárka Stejskalová: Prikry-type forcings

Dear all,

The seminar meets on Wednesday November 15th at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program:
Šárka Stejskalová — Prikry-type forcings

Best,
David

## Tomasz Natkaniec: Perfectly everywhere surjective but not Jones functions

Tuesday, November 14, 2017, 17:15
Wrocław University of Technology, 215 D-1

Speaker: Tomasz Natkaniec (University of Gdansk)

Title: Perfectly everywhere surjective but not Jones functions

Abstract:

Given a function $f:\mathbb{R}\to\mathbb{R}$ we say that

1. $f$ is perfectly surjective ($f\in \mathrm{PES}$) if $f[P]=\mathbb{R}$ for every perfect set $P$;
2. $f$ is a Jones function ($f\in\mathrm{J}$) if $C\cap f\neq\emptyset$ for every closed $C\subset\mathbb{R}^2$ with $\mathrm{dom}(C)$ of size $\mathfrak{c}$.

M. Fenoy-Munoz, J.L. Gamez-Merino, G.A. Munoz-Fernandez and E. Saez-Maestro in the paper ”A hierarchy in the family of real surjective functions” [Open Math. 15 (2017), 486–501] asked about the lineability of the set $\mathrm{PES}\setminus\mathrm{J}$.
Answering this question we show that the class $\mathrm{PES}\setminus\mathrm{J}$ is $\mathfrak{c}^+$-lineable. Moreover, if
$2^{<\mathfrak{c}}=\mathfrak{c}$ then $\mathrm{PES}\setminus\mathrm{J}$ is $2^\mathfrak{c}$-lineable. We prove also that the additivity number
$A(\mathrm{PES}\setminus\mathrm{J})$ is between $\omega_1$ and $\mathfrak{c}$. Thus $A(\mathrm{PES}\setminus\mathrm{J})=\mathfrak{c}$ under CH,
however this equality can't be proved in ZFC, because the Covering Property Axiom CPA implies $A(\mathrm{PES}\setminus\mathrm{J})=\omega_1<\mathfrak{c}$.

The talk is based on the joint paper:
K.C.Ciesielski, J.L. Gamez-Merino, T. Natkaniec, and J.B. Seoane-Sepulveda, '' On functions that are almost continuous and perfectly everywhere surjective but not Jones. Lineability and additivity'', submitted.

## Boriša Kuzeljević: Some applications of PID

Dear all,

The seminar meets on Wednesday November 8th at 11:00.

Program: Boriša Kuzeljević — Some applications of PID
The talk will be a continuation of the talk from the previous Wednesday.

Best,
David