Translator Disclaimer
December 2008 P-hierarchy on β ω
Andrzej Starosolski
J. Symbolic Logic 73(4): 1202-1214 (December 2008). DOI: 10.2178/jsl/1230396914

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

Download Citation

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

Information

Published: December 2008
First available in Project Euclid: 27 December 2008

zbMATH: 1156.03047
MathSciNet: MR2467212
Digital Object Identifier: 10.2178/jsl/1230396914

Subjects:
Primary: 2000 MSC: 54F65 , 54C99

Keywords: monotone sequential contour , ordinal ultrafilters , P-hierarchy , P-points

Rights: Copyright © 2008 Association for Symbolic Logic

JOURNAL ARTICLE
13 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.73 • No. 4 • December 2008
Back to Top