# 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?