## Chris Lambie-Hanson: Partition relations and generalized scattered orders

BIU seminar in Set Theory

On 30/03/2017, 10-12, Building 604, Room 103

Speaker: Chris Lambie-Hanson

Title: Partition relations and generalized scattered orders
Abstract: The class of scattered linear orders, isolated by Hausdorff, plays a prominent role in the study of general linear orders. In 2006, Dzamonja and Thompson introduced classes of orders generalizing the class of scattered orders. For a regular cardinal kappa, they defined the classes of kappa-scattered and weakly kappa-scattered linear orders. For kappa = omega, these two classes coincide and are equal to the classical class of scattered orders. For larger values of kappa, though, the two classes are provably different. In this talk, we will investigate properties of these generalized scattered orders with respect to partition relations, in particular the extent to which the classes of kappa-scattered or weakly kappa-scattered linear orders of size kappa are closed under partition relations of the form tau -> (phi, n) for n < omega. We will show that, assuming kappa^{<kappa} = kappa, the class of weakly kappa-scattered orders is closed under all such partition relations while, for uncountable values of kappa, the class of kappa-scattered orders consistently fails to be closed. Along the way, we will prove a generalization of the Milner-Rado paradox and look at some results regarding ordinal partition relations. This is joint work with Thilo Weinert.

## Chris Lambie-Hanson: Trees with ascent paths

HUJI Logic Seminar

The next meeting of the Logic Seminar will be in Wednesday, 22/03/17, 16:00 – 18:00, Ross buiding.

Speaker: Chris Lambie-Hanson

Title: Reflections on the coloring and chromatic numbers

Abstract: The notion of an ascent path through a tree, isolated by Laver, is a generalization of the notion of a cofinal branch and, in many cases, the existence of an ascent path through a tree provides a concrete obstruction to the tree being special. We will discuss some recent results regarding ascent paths through $\kappa$-trees, where $\kappa > \omega_1$ is a regular cardinal. We will discuss the consistency of the existence or non-existence of a special $\mu^+$-tree with a $cf(\mu)$-ascent path, where $\mu$ is a singular cardinal. We will also discuss the consistency of the statement, “There are $\omega_2$-Aronszajn trees but every $\omega_2$-tree contains an $\omega$-ascent path.” We will connect these topics with various square principles and with results about the productivity of chain conditions.

## Chris Lambie-Hanson: Reflections on the coloring and chromatic numbers

HUJI Logic Seminar

The next meeting of the Logic Seminar will be in Wednesday, 18/01, 16:00 – 18:00, Ross 70.
Speaker: Chris Lambie-Hanson

Title: Reflections on the coloring and chromatic numbers

Abstract: Compactness phenomena play a central role in modern set theory, and the investigation of compactness and incompactness for the coloring and chromatic numbers of graphs has been a thriving area of research since the mid-20th century,when De Bruijn and Erdős published their compactness theorem for finite chromatic numbers.

In this talk, we will briefly review some of the highlights in this area and then present new results indicating, firstly, that the coloring number can only exhibit a limit amount of incompactness, and, secondly, that large amounts of incompactness for the chromatic number are compatible with strong compactness statements, including compactness for the coloring number.
This is joint work with Assaf Rinot.

## Salma Kuhlmann: The Baer-Krull Theorem for Quasi-ordered fields

BGU Seminar in Logic, Set Theory and Topology

Tomorrow we continue our seminar in Logic, Set Theory and Topology.
Time: Tuesday, January 3, 12:15-13:30.
Place: Seminar room -101, Math building 58.
Speaker: Salma Kuhlmann (Konstantz)
Title: The Baer-Krull Theorem for Quasi-ordered fields
Abstract:
In my seminar talk on 29.12.2015, I introduced the notion of quasi-ordered fields, proved Fakhruddin’s dichotomy. In this talk, I will present a version of a classical theorem in real algebra (the Baer-Krull theorem) for quasi-ordered fields.

## Ludomir Newelski: Stable groups and topological dynamics

HUJI Logic Seminar

The next meeting of the Logic Seminar will be in Wednesday, 04/01/17, between 16:00 – 18:00, Ross 70.

Please forward this mail to anyone that might be interested.
Speaker: Ludomir Newelski
Title: Stable groups and topological dynamics

Abstract: Assume G is a stable group. I will recall an old 2-step theorem of mine on generating a type-definable subgroup of G by a single type. I will discuss some related questions and put them into context of topological dynamics.

## Itaï Ben Yaacov: Baby version of the asymptotic volume estimate

HUJI Logic Seminar

Tomorrow (27/12) we will have a lecture of Itaï Ben Yaacov in Sprinzak Building, between 10:00 – 12:00, room 102.

Please forward this mail to anyone that might be interested.

Baby version of the asymptotic volume estimate

Abstract: I’ll show how the Vandermonde determinant identity allows us to

estimate the volume of certain spaces of polynomials in one variable

(or rather, of homogeneous polynomials in two variables), as the degree

goes to infinity.

I’ll explain what this is good for in the context of globally valued

fields, and, given time constraints, may give some indications on the

approach for the “real inequality” in higher projective dimension.

## Assaf Rinot: Partitioning a cardinal into fat stationary sets

BIU seminar in Set Theory

On 29/12/2016, 10-12, Building 216, Room 201

Assaf Rinot

Partitioning a cardinal into fat stationary sets

A subset $F$ of a regular uncountable cardinal $\kappa$ is said to be fat iff for every club $C\subseteq\kappa$, and every ordinal $\alpha<\kappa$, $F\cap C$ contains a closed copy of $\alpha+1$.
By a theorem of H. Friedman from 1974, every stationary subset of $\omega_1$ is fat. In particular, $\omega_1$ may be partitioned into $\omega_1$ many pairwise disjoint fat sets.

In this talk, I shall prove that $\square(\kappa)$ implies that any fat subset of $\kappa$ may be partitioned into $\kappa$ many pairwise disjoint fat sets. In particular, the following are equiconsistent:

1. $\omega_2$ cannot be partitioned into $\omega_2$ many pairwise disjoint fat sets;
2. $\omega_2$ cannot be partitioned into two disjoint fat sets;
3. there exists a weakly compact cardinal.

## Matthew Foreman: Better lucky than smart: realizing a quasi-generic class of measure preserving transformations as diffeomorphisms

HUJI Logic Seminar

The next meeting of the Logic Seminar will be in Wednesday, 28/12/16, 16:00 – 18:00, in Ross Building, 70.

Title: Better lucky than smart: realizing a quasi-generic class of measure preserving transformations as diffeomorphisms.
Speaker: Matthew Foreman
Abstract: In 1932, von Neumann proposed classifying measure preserving diffeomorphisms up to measure isomorphism. Joint work with B. Weiss shows this is impossible in the sense that the corresponding equivalence relation is not Borel; hence impossible to capture using countable methods.

An accidental consequence of the proof addresses a different classical problem: which measure preserving transformations are isomorphic to diffeomorphisms of a compact smooth manifold?
In this talk we discuss the proof that  a quasi-generic class of measure preserving transformations are isomorphic to measure preserving diffeomorphisms of the torus.

## Asaf Karagila: Fodor’s lemma can fail at every cardinal

HUJI Logic Seminar
The next meeting of the Logic Seminar will take place in next Wednesday,
14/12, Ross Building 70, 16:00 — 18:00.

Speaker: Asaf Karagila

Title: Fodor’s lemma can fail at every cardinal
Abstract. Fodor’s lemma states that given a regressive function from an
uncountable regular $\kappa$ to itself must have a stationary fiber. We will
discuss the possible failure of this lemma at an arbitrary cardinal $\kappa$,
as well some provable facts about the club filters which are equivalent to
Fodor’s lemma in ZF. If time permits, we will outline two methods for
obtaining global failures.

This talk will be based on the paper: Fodor’s lemma can fail everywhere,
which can be found on arXiv, https://arxiv.org/abs/1610.03985

## Boris Zilber: Structural approximation.

HUJI Logic Seminar

The next meeting of the Logic Seminar will take place in Wednesday, 07/12, 16:00 – 18:00, in Ross Building 70.
Please forward this mail to anyone who might be interested in this talk (or in the seminar).

Structural approximation.

Speaker: Boris Zilber
Abstract. In the framework of positive model theory I will give (recall) a definition of “structural approximation”  which is used in my paper on model-theoretic interpretation of quantum mechanics. I will then present some general theory as well as a few examples.