P-Filters and the perfect set property

摘要

In this paper, we prove that every non-meager P-filter F is a PSP(Σ_1~1)-filter (that is, A ∩ F has the perfect set property whenever A is an analytic subset of 2~ω) and the filter product of a Ramsey ultraftlter and a P_(ω2)-point is a PSP(Σ_1~1)-ultrafilter. These theorems strengthen a result of Miller and answer some questions asked by Andrea Medini and David Milovich.