P-hierarchy on β ω

Journal of Symbolic Logic 73 (4):1202-1214 (2008)

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 {Pα}1≤α≤ω1 of disjoint classes. We prove that non-emptiness of Pα 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
Keywords P-hierarchy   P-points   monotone sequential contour   ordinal ultrafilters
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DOI 10.2178/jsl/1230396914
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