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.
Citation
Andrzej Starosolski. "P-hierarchy on β ω." J. Symbolic Logic 73 (4) 1202 - 1214, December 2008. https://doi.org/10.2178/jsl/1230396914
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