This paper presents a logical system in which various group-level epistemic actions are incorporated into the object language and contains the infinitary operators used in the standard modeling of common knowledge.Expand

We study in this paper graph coloring problems in the context of descriptive set theory. We consider graphs G=(X, R), where the vertex set X is a standard Borel space (i.e., a complete separable… Expand

We investigate the structure of Gδ ideals of compact sets. We define a class of Gδ ideals of compact sets that, on the one hand, avoids certain phenomena present among general Gδ ideals of compact… Expand

We study the σ-ideal of Haar null sets on Polish groups. It is shown that on a non-locally compact Polish group with an invariant metric this σ-ideal is closely related, in a precise sense, to the… Expand

All spaces considered are metric separable and are denoted usually by the letters X, Y, or Z. w stands for the set of all natural numbers. If a metric separable space is additionally complete, we… Expand

We give an algebraic characterization of those sequences (HnI) of countable abelian groups for which the equivalence relations induced by Borel (or, equivalently, continuous) actions of Ho x Hl x H2… Expand

We prove that in Polish, abelian, non-locally-compact groups the family of Haar null sets of Christensen does not fulfil the countable chain condition, that is, there exists an uncountable family of… Expand