This paper presents a logical system in which various group-level epistemic actions are incorporated into the object language. That is, we consider the standard modeling of knowledge among a set ofâ€¦ (More)

We study the structure of analytic ideals of subsets of the natural numbers. For example. we prove that for an analytic ideal I, either the ideal {X c w x CO: 3n X ~(0, 1.. ,n} x o} is Rudin-Keislerâ€¦ (More)

We prove the direct structural Ramsey theorem for structures with relations as well as functions. The result extends the theorem of Abramson and Harrington and of NeÅ¡etÅ™il and RÃ¶dl.

We prove that there is a GÎ´ Ïƒ-ideal of compact sets which is strictly above NWD in the Tukey order. Here NWD is the collection of all compact nowhere dense subsets of the Cantor set. This answers aâ€¦ (More)

We prove a Ramsey theorem for finite sets equipped with a partial order and a fixed number of linear orders extending the partial order. This is a common generalization of two recent Ramsey theoremsâ€¦ (More)

We give an algebraic characterization of those sequences {Hâ€ž) of countable abelian groups for which the equivalence relations induced by Borel (or, equivalently, continuous) actions of Hq x Hi x Hi xâ€¦ (More)

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 ofâ€¦ (More)