Ultrafilters and Decompositions of Abelian Groups

Abstract

We prove that every PS-ultrafilter on a group without second-order elements is a Ramsey ultrafilter. For an arbitrary PS-ultrafilter ϕ on a countable group G, we construct a mapping f: G → ω such that f(ϕ) is a P-point in the space ω*. We determine a new class of subselective ultrafilters, which is considerably wider than the class of PS-ultrafilters.