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P-hierarchy on βω

Published online by Cambridge University Press:  12 March 2014

Andrzej Starosolski
Andrzej Starosolski*
Affiliation:
Wydział Matematyczno-Fizyczny, Politechnika Ślaska, Gliwice, Poland, E-mail: andrzej.starosolski@polsl.pl
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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 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.

Keywords

P-hierarchyP-pointsmonotone sequential contourordinal ultrafilters
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 73 , Issue 4 , December 2008 , pp. 1202 - 1214
Copyright
Copyright © Association for Symbolic Logic 2008

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References

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