Martin Goldstern: Higher Random Reals

HUJI Logic Seminar
Tuesday 29/5 13:30-15:00 Ross 63
Title: Higher Random Reals
Speaker: Martin Goldstern
The set of real numbers is often identified with
Cantor Space 2^omega, with which it shares many important
properties: not only the cardinality, but also other
“cardinal characteristics” such as cov(null), the smallest
number of measure zero sets needed to cover the whole space,
and similarly cov(meager), where meager=”first category”;
or their “dual” versions non(meager) (the smallest
cardinality of a nonmeager set) and non(null).

Many ZFC results and consistency results (such as
“cov(meager) lessequal non(null), but no inequality between
cov(null) and cov(meager) is provable in ZFC”)
are known.

Recent years have seen a renewed interest in “higher reals”,
i.e., elements of 2^kappa, where kappa is usually an inaccessible
cardinal. Meager sets have a natural generalisation to this
context, namely “kappa-meager” sets (using the <kappa-box product
topology), but what is the natural generalisation of the
ideal of null sets?

In my talk I will present an ideal null_kappa recently introduced
by Saharon Shelah, and some ZFC and consistency results from a
forthcoming joint paper with Thomas Baumhauer and Saharon Shelah,
such as “cov(null_kappa) lessequal non(null_kappa)”, and
“consistently, cov(meager_kappa) > cov(null_kappa)”.

Otmar Spinas: Why Silver is special

Place:   Bahen Center BA6183

Date: May 25, 2018 (13:30-15:00)
Speaker: Otmar Spinas
Title:  Why Silver is special
Abstract: I will try to give some insight into the challenging combinatorics of two amoeba forcings, one for Sacks forcing, the other one for Silver forcing. They can be used two obtain some new consistencies of inequalities between the additivity and the cofinality coefficients of the associated forcing ideals which are the Marcewski and the Mycielski ideal, respectively, and of the ideals associated with Laver forcing and Miller forcing.

Borisha Kuzeljevic: P-ideal dichotomy and some versions of the Souslin Hypothesis

Talk held by Borisha Kuzeljevic (Czech Academy of Sciences, Prague) at the KGRC seminar on 2018-05-24.

Abstract: The talk will be about the relationship of PID with the statement that all Aronszajn trees are special. This is joint work with Stevo Todorcevic.

David Fernández-Bretón: Variations and analogs of Hindman’s theorem

Mathematical logic seminar – May 22 2018
Time:     3:30pm – 4:30 pm

Room:     Wean Hall 8220

Speaker:         David Fernández-Bretón
Department of Mathematics
University of Michigan

Title:     Variations and analogs of Hindman’s theorem


Hindman’s theorem is a Ramsey-theoretic result asserting that, whenever one colours the set of natural numbers with finitely many colours, there will be an infinite set such that all numbers that can be obtained by adding finitely many elements from the set (no repetitions allowed) have the same colour. I will explore generalizations and extensions of this theorem: replacing “natural numbers” with “abelian group” and varying the number of colours, as well as the size of the desired monochromatic set, yields a plethora of very interesting results.

Harry Altman: Lower sets in products of well-ordered sets and related WPOs

Thursday, May 24, 2018, from 4 to 5:30pm
East Hall, room 4096

Speaker: Harry Altman (University of Michigan)

Title: Lower sets in products of well-ordered sets and related WPOs


Following last week’s talk on maximum order types of well partial orders, we’ll compute the maximum order type of the set of bounded lower sets in N^m, as well as generalizations to finite products of other well-ordered sets, and discuss the maximum order types of some other related well partial orders also.

Damian Sobota: Rosenthal families and ultrafilters

Dear all,

The seminar meets on Wednesday May 23rd at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program: Damian Sobota — Rosenthal families and ultrafilters

Rosenthal’s lemma is a simple technical result with numerous
applications to measure theory and Banach space theory. The lemma in its
simplest form reads as follows: “For every infinite real-entried matrix
(m(n,k): n,k in N) such that every entry is non-negative and the sum of
every row is <=1, and every epsilon>0, there exists an infinite subset A
of N such that for every k in A we have sum_{n in A, n\neq
k}m_n^k<epsilon.” A natural question arises whether we can choose the
set A from a previously fixed family F of infinite subsets of N. If F
has such a property, then we call it Rosenthal. Thus, Rosenthal’s lemma
states that [N]^omega is Rosenthal. During my talk I’ll present some
necessary or sufficient conditions for a family to be Rosenthal and
prove that under MA(sigma-centered) there exists a P-point which is a
Rosenthal family but not a Q-point. (No Banach space will appear during
the talk.)


Alessandro Vignati: Homeomorphisms of Cech-Stone remainders

Place: Bahen Centre Information T (Room BA 2165)
Date: May 18, 2018 (13:30-15:00)
Speaker: Alessandro Vignati
Title: Homeomorphisms of Cech-Stone remainders
Abstract: From a locally compact space X one construct its Cech-Stone remainder X*=beta X minus X. We analyze the problem on whether X* and Y* can be homeomorphic for different spaces X and Y. In the 0-dimensional case, a solution to this problem has been proved to be independent of ZFC, by the work of Parovicenko, Farah, Dow-Hart and Farah-McKenney among others.
We prove, under PFA, the strongest possible rigidity result: for metrizable X and Y, we prove that X* is homeomorphic to Y* only if X and Y are homeomorphic modulo compact subsets. We also show that every homeomorphism X* –> Y* lifts to an homeomorphism between cocompact subsets of X and Y.

François Le Maître: Ample generics and full groups

Mathematical logic seminar – May 15 2018
Time:     3:30pm – 4:30 pm

Room:     Wean Hall 8220

Speaker:         François Le Maître
Institut de Mathématiques de Jussieu-PRG
Université Paris Diderot

Title:     Ample generics and full groups


In this talk, I will explain why the full group of the action of the rationals on the real line is an example of a connected topologically simple Polish group with ample generics, providing a natural answer to a question of A. Kechris and C. Rosendal. If time permits, I will discuss the following open question: is there a Polish group with ample generics which is not quasi non-archimedean ? The talk is based on a joint work with Adriane Kaïchouh.

Yair Hayut: Stationary reflection at $\aleph_{\omega+1}$

Talk held by Yair Hayut (Tel-Aviv University, Israel)
at the KGRC seminar on 2018-05-17.

Abstract: Stationary reflection is one of the basic prototypes of reflection phenomena,
and its failure is related to many counterexamples for compactness
properties (such as almost free non-free abelian groups,
and more). In 1982, Magidor showed that it is consistent, relative to infinitely many
supercomapct cardinals, that stationary reflections holds at $\aleph_{\omega + 1}$.
In this talk I’m going to present a new method for forcing stationary reflection
at $\aleph_{\omega+1}$, which allows to significantly reduce the upper bound for the consistency strength of the full stationary reflection at $\aleph_{\omega+1}$ (below a single partially supercompact cardinal).

This is a joint work with Spencer Unger.

Harry Altman: Well partial orderings and their maximum extending ordinals

Thursday, May 17, 2018, from 4 to 5:30pm
East Hall, room 4096

Speaker: Harry Altman (University of Michigan)

Title: Well partial orderings and their maximum extending ordinals


A well partial order is a partial order all of whose extensions to a total order are well-orders. (These are often studied as well-quasi-orders, where the requirement of antisymmetry is dropped.) In 1976 De Jongh and Parikh showed that for a given WPO X, among the ordinals obtained this way there is always a maximum o(X). We will discuss the theory of WPOs and o(X), several equivalent formulations, and how o(X) can actually be computed for some concrete WPOs.