P-hierarchy on β ω

Abstract

We classify ultrafilters on ω with respect to sequential contours (see [4], [5]) of different ranks. In this way we obtain an ω₁ sequence {𝒫_α}_{1≤ α ≤ ω₁} of disjoint classes. We prove that non-emptiness of 𝒫_α 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.