## Mirna Džamonja: Higher order versions of the logic of chains close

Dear all,

The seminar meets on Wednesday June 20th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program: Mirna Džamonja — Higher order versions of the logic of chains
close

First order logic of chains was discovered by Carol Karp and revisited
in recent work of Dz. with Jouko Vaananen. The results have shown that
the logic, defined through a singular cardinal of countable cofinality,
behaves very much like the first order logic. In our new joint work, we
study higher order versions of the logic of chains and their fragments
to defend the thesis that in this context we can also recover
similarities with the ordinary logic. We also discuss the idea of
infinite computation.

Best,
David

## Viera Šottová: Ideal version of selection principle S1(P,R)

The seminar meets on Wednesday June 6t at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Speaker: Viera Šottová

Title: Ideal version of selection principle $S_1(\mathcal P,\mathcal R)$.

Abstract: attached.

## 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.)

Best,
David

## Jonathan Verner: Ultrafilters and nonstandard models of arithmetic

Dear all,

The seminar meets on Wednesday May 9th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program: Jonathan Verner — Ultrafilters and nonstandard models of
arithmetic

(This is a talk postponed from April 18th.)

Best,
David

## Jonathan Verner: Ultrafilters and models of arithmetic

The seminar meets on Wednesday April 18th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program: Jonathan Verner — Ultrafilters and models of arithmetic

## Wojciech Wołoszyn: Laver-type posets

Dear all,

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

Program: Wojciech Wołoszyn will be presenting results about Laver type
posets from the paper of J. Zapletal and myself.

Best,
David

## Wednesday seminar: Andrew Brooke-Taylor

Dear all,

The seminar meets on Wednesday April 4th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

We will have a guest speaker Andrew Brooke-Taylor.

Best,
David

## Borisa Kuzeljevic: Isomorphic substructures of Fraisse limits

Dear all,

The seminar meets on Wednesday March 28th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program: Borisa Kuzeljevic — Isomorphic substructures of Fraisse limits

This is joint work with Milos Kurilic. For a relational structure X, its poset of copies is the set of all the substructures of X which are isomorphic to X, enlarged with the empty set, and ordered by inclusion. We will analyze posets of copies of various countable ultrahomogeneous structures. In particular, we will show that for many of these structures the class of order types of maximal chains of copies coincides with the class of order types of compact sets of reals with minimum non-isolated.

Best,
David

## 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.

## Jan Grebik: Applications of topological dynamics to graphons

The seminar meets on Wednesday February 28th at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program: Jan Grebik — Applications of topological dynamics to graphons
We show that the question about the existence of a Borel or continuous
lift for graphons has its counterpart in topological dynamics. We
present the optimal result in the general setting and then translate it
back to the original problem.