Weekly research seminar

2021-05-05, 16:15, Zoom

Jakub Andruszkiewicz (University of Warsaw)

It is a well-known fact that the diamond principle implies CH, but the reverse implication does not hold. The situation for successor cardinals larger than the first uncountable cardinal is quite different - as proved by Shelah, if only cardinal kappa is uncountable, then 2^kappa = kappa^+ is enough...

2021-04-28, 16:15, Zoom

Piotr Zakrzewski (University of Warsaw)

**On countably perfectly meager sets**We study a strengthening of the notion of a perfectly meager set. We say that that a subset A of a perfect Polish space X is countably perfectly meager in X if for every sequence (P_n) of perfect subsets of X, there is an F_sigma set F in X containing A and such that the intersection of F with P_n i...

2021-04-21, 16:15, Zoom

Piotr Borodulin-Nadzieja (University of Wrocław)

**On forcing names for ultrafilters**We show a way to handle names for ultrafilters in the random forcing. Using this approach we reprove Kunen's theorem about long towers in the random model and Kamburelis' characterization of Boolean algebras supporting finitely additive measures. The talk represents joint works with Dami...

2021-04-14, 16:15, Zoom

Ziemowit Kostana (University of Warsaw)

**What would the rational Urysohn space and the random graph look like if they were uncountable?**We apply the technology developed in the 80s by Avraham, Rubin, and Shelah, to prove that the following is consistent with ZFC: there exists an uncountable, separable metric space X with rational distances, such that every uncountable partial 1-1 function from X to X is an isometry on an uncountable...

2021-03-24, 16:15, Zoom

Grzegorz Plebanek (University of Wrocław)

**Weakly Radon-Nikodym Boolean algebras**Weakly Radon-Nikodym (WRN) Boolean algebras are named after a certain class of compacta related to Banach spaces but they can be charaterized as those algebras that have, in a sense, few independent sequences. We compare the class of WRN algebras with some others, such as minimally generated algebra...

2021-03-17, 16:15, Zoom

Damian Głodkowski (University of Warsaw)

**Coverings of Banach spaces and their subsets by hyperplanes**A hyperplane of a Banach space is a closed one-codimensional subspace. Hyperplanes are nowhere dense and so, no countable collection of hyperplanes can cover the entire space. Given a Banach space we consider the \sigma-ideal of all of its subsets which are covered by countably many hyperplanes and ...

2021-03-10, 16:15, Zoom

Piotr Koszmider (Institute of Mathematics of the Polish Academy of Sciences)

**A Banach space induced by an almost disjoint family, admitting only few operators and decompositions**We consider the closed linear subspace X(A) of the Banach space of real bounded sequences (l_infinity) generated by sequences converging to zero (c_0) and the characteristic functions of elements of an uncountable, almost disjoint family A of infinite subsets of N. This Banach spac...

2021-03-03, 16:15, Zoom

Marcin Sabok (McGill University)

**Probabilistic programming semantics for name generation**Abstract: I will discuss a recent result connecting the nu-calculus (which is an extension of simply-typed lambda calculus modelling the so-called "name generation") with a recent model for probabilistic programming, called the quasi-Borel spaces. There is a natural interpretation of the n...

2021-01-27, 16:15, Zoom

Aleksandra Kwiatkowska (University of Wrocław)

**The automorphism group of the random poset**A number of well-studied properties of Polish groups concern the interactions between the topological and algebraic structure of those groups. Examples of such properties are the small index property, the automatic continuity, and the Bergman property. An important approach for proving them is showi...

2021-01-20, 16:15, Zoom

Adam Bartoš (Institute of Mathematics of the Czech Academy of Sciences)

**Approximate Fraïssé theory and MU-categories**Fraïssé theory links together properties of families of structures like the amalgamation property with properties of limit objects like homogeneity and the extension property. The structures considered are not limited to be first-order structures, and the maps between the structures are ...