## Bill Chen: A small Dowker space

BIU seminar in Set Theory

Speaker: Bill Chen (BGU)

There will be two talks: November 27 and December 4.

First talk: A small Dowker space, part 1

Abstract. A topological space is said to be “Dowker” if it is normal but its product with the unit interval is not normal. In this lecture, we shall present a construction, due to Balogh, of a Dowker space of size continuum.

Second talk: A small Dowker space, part 2

Abstract. Last week, we presented an approach for constructing a Dowker space of size continuum, ending up with a statement of a lemma that would yield such a space. In this talk, we shall prove this lemma.

## 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.

## 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.

## Itai Ben Yaacov: Reconstruction for non-aleph0-categorical theories?

HUJI Logic Seminar

This Wednesday, 8 November, we will have a meeting of the Logic Seminar. The meeting will be in Math 209, 8 November (Wednesday), 11:00 – 13:00.

Speaker: Itai Ben Yaacov
Title: Reconstruction for non-aleph0-categorical theories?

Abstract. It is a familiar fact (sometimes attributed to Ahlbrandt-Ziegler, though it is possibly older) that two aleph0-categorical theories are bi-interpretable if and only if their countable models have isomorphic topological isomorphism groups. Conversely, groups arising in this manner can be given an abstract characterization, and a countable model of the theory (up to bi-interpretation, of course) can be reconstructed.
More recently, it was observed that various (interpretation-invariant) properties of an aleph0-categorical theory (stability, NIP, …) correspond to familiar dynamical properties of the automorphism group, with a few nice applications.
Since stability and NIP have nothing to do with aleph0-categoricity, one may ask whether the correspondence between theories (up to bi-interpretation) and topological groups can be extended to theories which are not aleph0-categorical? There are some indications that a positive answer is possible, if one is willing to replace groups with more general objects.
See you there,
Yatir

## 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.

## 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.

## Shimon Garti: The club principle and the splitting number

HUJI Logic Seminar
The next meeting of the Logic Seminar will take place Wednesday, 28/06, 16:00 – 18:00, Ross 70.  This is the last meeting of the Logic Seminar for this semester.
Speaker: Shimon Garti
Title: Tiltan
Abstract: We shall try to prove some surprising (and hopefully, correct) theorems about the relationship between the club principle (Hebrew: tiltan) and the splitting number, with respect to the classical s at omega and the generalized s at supercompact cardinals.

## Bill Chen: Variations of the stick principle

BGU seminar in Logic, Set Theory and Topology

Time: Tuesday, June 27th, 12:15-13:30.
Place: Seminar room -101, Math building 58.
Speaker: Bill Chen (BGU)

Title: Variations of the stick principle

Abstract:
The stick principle asserts that there is a family of infinite subsets of $\omega_1$ of size $\aleph_1$ so that any uncountable subset of $\omega_1$ has some member of the family as a subset. We will give a forcing construction to separate versions of the stick principle which put a bound on the order-type of the subsets in the family. Time permitting, we will say a little about the relation of the stick principle with the existence of Suslin trees.

## Ari Brodsky: ​Constructing free Souslin trees from a proxy principle

BGU seminar in Logic, Set Theory and Topology

Time: Tuesday, June 13th, 12:15-13:30.
Place: Seminar room -101, Math building 58.
Speaker: ​Ari Brodsky (BIU)

Title: ​Constructing free Souslin trees from a proxy principle

Abstract. ​More than 40 years ago, Jensen constructed a free Souslin tree of height $\omega_1$ from $\diamondsuit(\omega_1)$.
We show how to construct a free $\kappa$-Souslin tree, where $\kappa$ is an arbitrary regular uncountable cardinal.
This is joint work with Assaf Rinot.​

## Thilo Weinert: Avoiding Quadruples Using a Scale

BIU seminar in Set Theory

On 08/06/2017, 10-12, Building 604, Room 103

Speaker: Thilo Weinert (BGU)

Title: Avoiding Quadruples Using a Scale

Abstract. In 1971, Hajnal showed that the continuum hypothesis implies omega_1^2 -|-> (omega_1^2, 3)^2 and in the same year, together with Erdős, that GCH implies that for every infinite cardinal kappa and every alpha < (kappa^+)^2 we have alpha -|-> (kappa^+ * kappa, 3)^2. In the same paper they showed that for infinite cardinals kappa and alpha < (kappa^+)^2 we have (kappa^+)^2 —> (alpha, 3)^2. In 1987, together with Baumgartner, he showed that for regular kappa satisfying 2^kappa = kappa^+ = lambda we have lambda^2 -|-> (lambda * kappa, 4)^2.

In 1998, Jean Larson showed that for regular kappa and lambda = kappa^+ the existence of a scale of length lambda of functions f : kappa — > kappa implies the failure of the aforementioned partition relations shown to
be unprovable from ZFC in the seventies, i.e. lambda * kappa —> (lambda * kappa, 3)^2 and lambda^2 —> (lambda^2, 3)^2. She commented that it would be interesting to know whether this hypothesis also suffices to prove lambda^2 -|-> (lambda * kappa, 4)^2.

It does.