Theory of sets: model in $ mathsf {ZFC} $ without points $ P $ nor points Q $

A $ P $-point is an ultrafilter $ scr U $in $ omega $ such that for each function $ f: omega to omega $ There is $ x en { scr U} $ such that the restriction $ f | _x $ It is constant or injective.

A $ Q $-point is an ultrafilter $ scr U $in $ omega $ such that for each function $ f: omega to omega $ with the property that $ f ^ {- 1} ( {m }) $ it is finite for each $ m en omega $, There is $ x en { scr U} $ such that the restriction $ f | _x $ he is injective.

$ P $-points do not need to exist, and $ Q $-Points do not need to exist.

Question. It is possible that none $ P $– neither $ Q $-points exist?