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2012 Thin Ultrafilters
O. Petrenko, I. V. Protasov
Notre Dame J. Formal Logic 53(1): 79-88 (2012). DOI: 10.1215/00294527-1626536

Abstract

A free ultrafilter $\mathcal{U}$ on $\omega$ is called a $T$-point if, for every countable group $G$ of permutations of $\omega$, there exists $U\in\mathcal{U}$ such that, for each $g\in G$, the set $\{x\in U:gx\ne x, gx\in U\}$ is finite. We show that each $P$-point and each $Q$-point in $\omega^*$ is a $T$-point, and, under CH, construct a $T$-point, which is neither a $P$-point, nor a $Q$-point. A question whether $T$-points exist in ZFC is open.

Citation

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O. Petrenko. I. V. Protasov. "Thin Ultrafilters." Notre Dame J. Formal Logic 53 (1) 79 - 88, 2012. https://doi.org/10.1215/00294527-1626536

Information

Published: 2012
First available in Project Euclid: 9 May 2012

zbMATH: 1258.03057
MathSciNet: MR2925270
Digital Object Identifier: 10.1215/00294527-1626536

Subjects:
Primary: 54D35, 54D80

Rights: Copyright © 2012 University of Notre Dame

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Vol.53 • No. 1 • 2012
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