Category Archives: Seminars

David Chodounsky: How to kill a P-point

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 14 March 2018, 17:00 hrs

Room: S17#04-06, Department of Mathematics, NUS

Speaker: David Chodounsky

Title: How to kill a P-point


The existence of P-points (also called P-ultrafilters) is independent
of the axioms of set theory ZFC. I will present the basic ideas behind
a new and simple proof of the negative direction of this fact; a new
forcing method for destroying P-points.

Thilo Weinert: Cardinal Characteristics and Partition Properties

Talk held by Thilo Weinert (KGRC) at the KGRC seminar on 2018-03-15.

Abstract: Many a partition relation has been proved assuming the Generalised Continuum Hypothesis. More precisely, many negative partition relations involving ordinals smaller than $\omega_2$ have been proved assuming the Continuum Hypothesis. Some recent results in this vein for polarised partition relations came from Garti and Shelah. The talk will focus on classical partition relations. The relations $\omega_1\omega  \not\rightarrow (\omega_1\omega, 3)^2$ and $\omega_1^2 \not\rightarrow (\omega_1\omega, 4)^2$ were both shown to follow from the Continuum Hypothesis, the former in 1971 by Erdős and Hajnal and the latter in 1987 by Baumgartner and Hajnal.

The former relation was shown to follow from both the dominating number and the stick number being $\aleph_1$ in 1987 by Takahashi. In 1998 Jean Larson showed that simply the dominating number being $\aleph_1$ suffices for this. It turns out that the unbounding number and the stick number both being $\aleph_1$ yields the same result. Moreover, also the second relation follows both from the dominating number being  $\aleph_1$ and from both the unbounding number and the stick number being $\aleph_1$ thus answering a question of Jean Larson.

This is both joint work with Chris Lambie-Hanson and with both William Chen and Shimon Garti.

David J. Fernández Bretón: Models of set theory with union ultrafilters and small covering of meagre, II

Thursday, March 15, 2018, from 4 to 5:30pm
East Hall, room 3088

Speaker: David J. Fernández Bretón (University of Michigan)

Title: Models of set theory with union ultrafilters and small covering of meagre, II


Union ultrafilters are ultrafilters that arise naturally from Hindman’s finite unions theorem, in much the same way that selective ultrafilters arise from Ramsey’s theorem, and they are very important objects from the perspective of algebra in the Cech–Stone compactification. The existence of union ultrafilters is known to be independent from the ZFC axioms (due to Hindman and Blass–Hindman), and is known to follow from a number of set-theoretic hypothesis, of which the weakest one is that the covering of meagre equals the continuum (this is due to Eisworth). In the first part of this two-talk series I exhibited a model of ZFC with union ultrafilters whose covering of meagre is strictly less than the continuum, obtained by means of a short countable support iteration. In this second talk, I will exhibit two more such models, one obtained by means of a countable support iteration of proper forcings, and the other by means of a single-step forcing (modulo being able to obtain an appropriate ground model).

Yasser Fermán Ortiz Castillo: Crowded pseudocompact spaces of cellularity at most the continuum are resolvable

Place: Fields Institute (Room 210)

Date: March 9 , 2018 (13:30-15:00)

Speaker: Yasser Fermán Ortiz Castillo

Title: Crowded pseudocompact spaces of cellularity at most the continuum are resolvable

Abstract: It is an open question from W. Comfort and S. Garcia-Ferreira if it is true that every crowded pseudocompact space is resolvable. In this talk will be present a partial positive answer for spaces of cellularity at most the continuum.

Grzegorz Plebanek: On almost disjoint families with property (R)

Tuesday, March 13, 2018, 17:15
Wrocław University of Technology, 215 D-1

Speaker: Grzegorz Plebanek (University of Wroclaw)

Title: On almost disjoint families with property (R)


We consider (with A.Aviles and W. Marciszewski) almost disjoint families with some combinatorial property that has applications in functional analysis. We are looking for the minimal cardinality of m.a.d. family with property (R). It turns out that this cardinal is not greater than $non(\mathcal{N})$ the uniformity of null sets.

Šárka Stejskalová – The tree property and the continuum function

Talk held by Šárka Stejskalová (KGRC) at the KGRC seminar on 2018-03-08.

Abstract: We will discuss the tree property, a compactness principle which can hold at successor cardinals such as $\aleph_2$ or $\aleph_3$. For a regular cardinal $\kappa$, we say that $\kappa$ has the tree property if there are no $\kappa$-Aronszajn trees. It is known that the tree property has the following non-trivial effect on
the continuum function:

(*) If the tree property holds at $\kappa^{++}$, then $2^\kappa> \kappa^+$.

After defining the key notions, we will review some basic constructions related to the tree property and state some original results regarding the tree property which suggest that (*) is the only restriction which the tree property puts on the continuum function in addition to the usual restrictions provable in ZFC.

Dana Bartosova: Ellis’ problem for automorphism groups

Thursday, March 8, 2018, from 4 to 5:30pm
East Hall, room 3088

Speaker: Dana Bartosova (Carnegie Mellon University)

Title: Ellis’ problem for automorphism groups


Ellis’ problem is a problem from topological dynamics asking whether two well studied flows are canonically isomorphic. In the case of groups of automorphisms of discrete structures, we can translate this problem into a question about Boolean algebras and solve the problem for some countable structures. We also arrive at questions about existence of certain ultrafilters. This is a join work with Andy Zucker.

Generalised Baire Spaces, Amsterdam, August 22-24, 2018

KNAW Academy Colloquium

Generalised Baire Spaces

Amsterdam, The Netherlands

Master Class: 22 August 2018 / Colloquium: 23–24 August 2018

Organisers. Lorenzo Galeotti, Benedikt Löwe, Philipp Lücke.
Descriptive set theory and set theory of the reals traditional deal with well-known and well-studied topological spaces such as the real numbers, Cantor space, and Baire space. In recent years, set theorists are increasingly interested in the uncountable analogues 2κ of the Cantor space (generalised Cantor space) and κκ of the Baire space (generalised Baire space) for uncountable cardinals κ.

While many concepts from the classical setting can be transferred to generalised Baire space and some classical results remain true at uncountable cardinals, in general the rich combinatorial nature of uncountable cardinals causes the theory of the corresponding spaces to differ significantly e.g., notions which are equivalent in the classical setting can lead to different notions in the generalised theory. Phenomena like this shed light on structures and properties otherwise hidden in the classical setting.

The study of generalised Baire spaces has developed into a research area in its own right with a rich overarching theory, internally motivated open questions (cf. Khomskii, Laguzzi, Löwe, Sharankou 2016) and an active research community, combining methods and techniques from several branches of set theory like uncountable combinatorics, forcing, large cardinals, inner models and classical descriptive set theory and also involves techniques from classical model theory. The community met first at the Amsterdam Set Theory Workshop 2014 in November 2014, then at a satellite workshop to the German mathematics congress in Hamburg in September 2015, and finally at a workshop at the Hausdorff Center for Mathematics in Bonn in September 2016. This Academy Colloquium is a reunion of the community after a hiatus of two years.

The Colloquium will be preceded by an associated KNAW Master Class for postgraduate students in order to prepare them for the talks at the Colloquium. The KNAW Master Class will take place on 22 August 2018.



Bruno Braga: On the rigidity of uniform Roe algebras of coarse spaces

Place: Fields Institute (Room 210)

Date: March 2 , 2018 (13:30-15:00)

Speaker: Bruno Braga

Title: On the rigidity of uniform Roe algebras of coarse spaces.

Abstract: (joint with Ilijas Farah) Given a coarse space (X,E), one can define a $C^*$-algebra $C^∗_u(X)$ called the uniform Roe algebra of (X,E). It has been proved by J. \v{S}pakula and R. Willet that if the uniform Roe algebras of two uniformly locally finite metric spaces with property A are isomorphic, then the metric spaces are coarsely equivalent to each other. In this talk, we look at the problem of generalizing this result for general coarse spaces and on weakening the hypothesis of the spaces having property A.

Adam Bartoš: Compactifiable classes and Borel complexity up to the equivalence

The seminar meets on Wednesday March 7th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program: Adam Bartoš — Compactifiable classes and Borel complexity up
to the equivalence
We discuss the notion of compact composition of a class of metrizable
compacta, and a general question of compactifiability of a given class.
This is connected to the Borel complexity of subsets of the hyperspace
of all metrizable compacta, up to the equivalence of classes.