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 of agents by multi-modal Kripke structures. One might want to consider actions that take place, such as announcements to groups privately, announcements withâ€¦ (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-Keisler below I, or Z is very simply induced by a lower semicontinuous submeasure. Also, we show that the class of ideals induced in this manner by lsc submeasuresâ€¦ (More)

We prove that arbitrary homomorphisms from one of the groups Homeo(2), Homeo(2), Aut(Q, <), Homeo(R) or Homeo(S) into a separable group are automatically continuous. This has consequences for the representations of these groups as discrete groups. For example, it follows, in combination with a result of V. G. Pestov, that any action of the discrete groupâ€¦ (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.