# Category Archives: Seminars

## Paul Szeptycki: Ladder systems after forcing with a Suslin tree

Place: Fields Institute (Room 210)

Date: November 24, 2017 (13:30-15:00)

Speaker: Paul Szeptycki

Title: Ladder systems after forcing with a Suslin tree

Abstract: Uniformization properties of ladder systems in models obtained by forcing with a Suslin tree S over a model of MA(S) are considered.

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

Thursday, November 30, 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 (II)

Abstract:

On this second talk I begin with Solovay’s characterization of real-valued measurability in terms of generic elementary embeddings, and build on results of Judah to prove that if there is an atomlessly measurable cardinal, then all (boldface) Delta-1-3 sets of reals are Lebesgue measurable. This is optimal in two respects: Just from the existence of measurable cardinals we cannot prove that lightface Delta-1-3 sets are measurable, and there are models with atomlessly measurable cardinals where there is a non-measurable Sigma-1-3 set. I will also discuss some related results.

## Merlin Carl: Complexity theory for ordinal Turing machines

Monday, November 27, 2017, 16.30
Seminar room 0.008, Mathematical Institute, University of Bonn

Speaker: Merlin Carl (Universität Konstanz)

Title: Complexity theory for ordinal Turing machines

Abstract:

Ordinal Turing Machines (OTMs) generalize Turing machines to transfinite working time and space. We consider analogues of theorems from complexity theory for OTMs, among them the Cook-Levin theorem, the P vs. NP problem and Ladner’s theorem. This is joint work with Benedikt Löwe and Benjamin Rin.

## Philipp Schlicht: The Hurewicz dichotomy for definable subsets of generalized Baire spaces

Monday, November 20, 2017, 16.30
Seminar room 0.008, Mathematical Institute, University of Bonn

Speaker: Philipp Schlicht (Universitat Bonn)

Title: The Hurewicz dichotomy for definable subsets of generalized Baire spaces

## 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.