P-Filters and the perfect set property

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 ultrafilter and a P ω 2 -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.