How high can Baumgartner's \cal I-ultrafilters lie in the P-hierarchy?

2011/08/08 by Machura, Michał, Starosolski, Andrzej
#03E05 #03E50 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1108.1818

Abstract

Under CH we prove that for any tall ideal \cal I on ω and for any ordinal γ≤ ω₁ there is an \cal I-ultrafilter (in the sense of Baumgartner), which belongs to the class \cal P_γ of P-hierarchy of ultrafilters. Since the class of \cal P₂ ultrafilters coincides with a class of P-points, out result generalize theorem of Flašková, which states that there are \cal I-ultrafilters which are not P-points.

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