Marcin Michalski: Bernstein, Luzin and Sierpiński meet trees

Tuesday, November 28, 2017, 17:15
Wrocław University of Science and Technology, 215 D-1

Speaker: Marcin Michalski (Wrocław University of Science and Technology)

Title: Bernstein, Luzin and Sierpiński meet trees

Abstract:

In [2] we have proven that if $\mathfrak{c}$ is a regular cardinal number, then the algebraic sum of a generalized Luzin set and a generalized Sierpiński set belongs to Marczewski ideal $s_0$. We will generalize this result for other tree ideals – $m_0$ and $l_0$ – using some lemmas on special kind of fusion sequences for trees of respective type.
Let us introduce a following notion. Let $\mathbb{X}$ be a set of trees.
Definition. We call a set $B$ a $\mathbb{X}$-Bernstein set, if for each $X\in\mathbb{X}$ we have $[X]\cap B\neq\emptyset$.
We shall explore this notion for various set of trees, including Sacks, Miller and Laver trees, with the support of technics developed in [1].

[1] Brendle J., Strolling through paradise, Fundamenta Mathematicae, 148 (1995), pp. 1-25.
[2] Michalski M., Żeberski Sz., Some properties of I-Luzin, Topology and its Applications, 189 (2015), pp. 122-135.

Yair Hayut: Chang’s Conjecture at many cardinals simultaneously

HUJI Logic Seminar
This Wednesday, 22 November, we will have a meeting of the Logic Seminar. The meeting will be in Math 209, 22 November (Wednesday), 11:00 – 13:00.

 
Speaker: Yair Hayut
Title: Chang’s Conjecture at many cardinals simultaneously

Abstract. Chang’s Conjecture is a strengthening of Lowenheim-Skolem-Tarski theorem. While Lowenheim-Skolem-Tarski theorem is provable in ZFC, any instance of Chang’s Conjecture is independent with ZFC and has nontrivial consistency strength. Thus, the question of how many instances of Chang’s Conjecture can consistently hold simultaneously is natural.
I will talk about some classical results on the impossibility of some instances of Chang’s Conjecture and present some results from a joint work with Monroe Eskew.

Toby Meadows: A Step Back from Forcing

Time: Mon, 11/27/2017 – 4:00pm – 5:30pm
Location: RH 440R

Speaker: Toby Meadows (University of Queensland)

Title: A Step Back from Forcing

Abstract. In this talk, I’ll sketch a way of unifying a wide variety of set theoretic approaches for generating new models from old models. The underlying methodology will draw from techniques in Sheaf Theory and the theory of Boolean Ultrapowers.

Sakae Fuchino: Downward Löwenheim-Skolem Theorems in stationary logic

Tuesday, November 21, 2017, 17:15
Wrocław University of Technology, 215 D-1

Speaker: Sakae Fuchino (Kobe University)

Title: Downward Löwenheim-Skolem Theorems in stationary logic

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 condensation 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 condensation 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)

Links to previous meetings:

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).