10 citations · 57 across the 21 of their papers we have counts for
12 papers · 1 filter
The uniform Gardner conjecture and rounding Borel flows
Matthew Bowen, Gábor Kun, Marcin Sabok
We study groups which satisfy Gardner's equidecomposition conjecture for uniformly distributed sets. We prove that an amenable group has this property if and only if it does not ad…
Measurable Hall's theorem for actions of abelian groups
Tomasz Cieśla, Marcin Sabok
We prove a measurable version of the Hall marriage theorem for actions of finitely generated abelian groups. In particular, it implies that for free measure-preserving actions of s…
The Hrushovski property for hypertournaments and profinite topologies
Jingyin Huang, Michael Pawliuk, Marcin Sabok +1
We study the problem of extending partial isomorphisms for hypertournaments, which are relational structures generalizing tournaments. This is a generalized version of an old quest…
On the complexity of topological conjugacy of Toeplitz subshifts
Marcin Sabok, Todor Tsankov
In this paper, we study the descriptive set theoretic complexity of the equivalence relation of conjugacy of Toeplitz subshifts of a residually finite group . On the one hand, w…
Automatic continuity for isometry groups
Marcin Sabok
We present a general framework for automatic continuity results for groups of isometries of metric spaces. In particular, we prove automatic continuity property for the group of is…
Topological representations
Adam Kwela, Marcin Sabok
This paper studies the combinatorics of ideals which recently appeared in ergodicity results for analytic equivalence relations. The ideals have the following topological represent…
Bounded forcing axioms and Baumgartner's conjecture
David Aspero, Sy-David Friedman, Miguel Angel Mota +1
We study the spectrum of forcing notions between the iterations of -closed followed by ccc forcings and the proper forcings. This includes the hierarchy of -proper forcings f…
Complexity of Ramsey null sets
Marcin Sabok
We show that the set of codes for Ramsey positive analytic sets is -complete. This is a one projective-step higher analogue of the Hurewicz theorem saying that the se…
Forcing properties of ideals of closed sets
Marcin Sabok, Jindrich Zapletal
With every -ideal on a Polish space we associate the -ideal generated by the closed sets in . We study the forcing notions of Borel sets modulo the respective $σ…
Forcing, games and families of closed sets
Marcin Sabok
We propose a new, game-theoretic, approach to the idealized forcing, in terms of fusion games. This generalizes the classical approach to the Sacks and the Miller forcing. For defi…
A note on ccc forcings
Marcin Sabok
The aim of this short note is to communicate a simple solution to the problem posed in [1] as Question 7.2.7: is it true that for every ccc -ideal I any I-positive Borel set con…
-continuity and related forcings
Marcin Sabok
The Steprans forcing notion arises as a quotient of Borel sets modulo the ideal of -continuity of a certain Borel not -continuous function. We give a characterization of this…