P-hierarchy on βω

Abstract

AbstractWe classify ultrafilters on ω with respect to sequential contours (see [4]. [5]) of different ranks. In this way we obtain an ω1 sequence of disjoint classes. We prove that non-emptiness of for successor α ≥ 2 is equivalent to the existence of P-point. We investigate relations between P-hierarchy and ordinal ultrafilters (introduced by J. E. Baumgartner in [1]). we prove that it is relatively consistent with ZFC that the successor classes (for α ≥ 2) of P-hierarchy and ordinal ultrafilters intersect but are not the same.