P-filters and Cohen, random, and Laver forcing

We answer questions about P-filters in the Cohen, random, and Laver forcing extensions of models of CH. In the case of the aleph(2)-random real poset, we prove that if square(aleph 1) also holds in the ground model, then there are P-points of omega* in the extension. The majority of the paper investigates the question of whether omega* can be covered by nowhere dense P-sets. We prove that this is not the case if aleph(2)-Cohen reals are added to a model of CH in which square(omega 1) holds, and that it is the case in the standard Laver extension. We also answer questions formulated by P. Nyikos about interactions between ultrafilter orderings of omega(omega) and mod finite scales. We show they have connections to ultrafilters having non-meager P-subfilters. (C) 2020 Elsevier B.V. All rights reserved.