P-Filters and the perfect set property

In this paper, we prove that every non-meager P-filter FF is a PSP(Σ11)-filter (that is, A∩FA∩F has the perfect set property whenever A   is an analytic subset of 2ω2ω) and the filter product of a Ramsey ultrafilter and a Pω2Pω2-point is a PSP(Σ11)-ultrafilter. These theorems strengthen a result of Miller and answer some questions asked by Andrea Medini and David Milovich.