10 citations · 22 across the 12 of their papers we have counts for
14 papers
Idealistic equivalence relations and the Lusin derivative
Bilge Köksal, Mateusz Lichman, Sławomir Solecki
We give a proof, that does not rely on analytic determinacy, of the existence of an idealistic analytic equivalence relation with Borel classes that is not classwise Borel isomorph…
Groups without unitary representations, submeasures, and the escape property
Friedrich Martin Schneider, Sławomir Solecki
We give new examples of topological groups that do not have non-trivial continuous unitary representations, the so-called exotic groups. We prove that all groups of the form $L^0(ϕ…
Polish modules over subrings of
Dexuan Hu, Sławomir Solecki
We give a method of producing a Polish module over an arbitrary subring of from an ideal of subsets of and a sequence in . The method allows us t…
Logics for Epistemic Actions: Completeness, Decidability, Expressivity
Alexandru Baltag, Lawrence S. Moss, Slawomir Solecki
We consider dynamic versions of epistemic logic as formulated in Baltag and Moss "Logics for epistemic programs" (2004). That paper proposed a logical language (actually families o…
The spectral form of Koopman representations of the group of measurable functions with values in the circle
Justin Tatch Moore, Sławomir Solecki
We compute the spectral form of the Koopman representation induced by a natural boolean action of identified earlier by the authors. Our computation establish…
Generic measure preserving transformations and the closed groups they generate
Sławomir Solecki
We show that, for a generic measure preserving transformation , the closed group generated by is not isomorphic to the topological group of all Lebesgu…
Tukey order among ideals
Jialiang He, Michael Hrušák, Diego Rojas-Rebolledo +1
We investigate the Tukey order in the class of ideals of subsets of . We show that no nontrivial ideal is Tukey below a ideal of compact sets. We introduce the…
The generic combinatorial simplex
Aristotelis Panagiotopoulos, Sławomir Solecki
We employ projective Fraïssé theory to define the "generic combinatorial -simplex" as the pro-finite, simplicial complex that is canonically associated with a family of simply d…
Transfinite sequences of topologies, descriptive complexity, and approximating equivalence relations
Sławomir Solecki
We introduce the notion of filtration between topologies and study its stabilization properties. Descriptive set theoretic complexity plays a role in this study. Filtrations lead t…
Concentration of measure, classification of submeasures, and dynamics of
Friedrich Martin Schneider, Sławomir Solecki
Exhibiting a new type of measure concentration, we prove uniform concentration bounds for measurable Lipschitz functions on product spaces, where Lipschitz is taken with respect to…
A combinatorial model for the Menger curve
Aristotelis Panagiotopoulos, Slawomir Solecki
We represent the universal Menger curve as the topological realization of the projective Fraïssé limit of the class of all finite connected graphs. We…
Coherent extension of partial automorphisms, free amalgamation, and automorphism groups
Daoud Siniora, Sławomir Solecki
We give strengthened versions of the Herwig-Lascar and Hodkinson-Otto extension theorems for partial automorphisms of finite structures. Such strengthenings yield several combinato…
Monoid actions and ultrafilter methods in Ramsey theory
Sławomir Solecki
First, we prove a theorem on dynamics of actions of monoids by endomorphisms of semigroups. Second, we introduce algebraic structures suitable for formalizing infinitary Ramsey sta…
Closed subgroups generated by generic measure automorphisms
Slawomir Solecki
We prove that for a generic measure preserving transformation , the closed group generated by is a continuous homomorphic image of a closed linear subspace of $L_0(λ,{\mathb…