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March 2012 Splitting stationary sets in $\mathscr{P}(\lambda)$
Toshimichi Usuba
J. Symbolic Logic 77(1): 49-62 (March 2012). DOI: 10.2178/jsl/1327068691

Abstract

Let $A$ be a non-empty set. $A$ set $S \subseteq \mathscr{P}(A)$ is said to be stationary in $\mathscr{P}(A)$ if for every $f: [A]^{< \omega} \to A$ there exists $ x \in S$ such that $x \neq A$ and $f"[x]^{<\omega}$. In this paper we prove the following: For an uncountable cardinal ? and a stationary set S in $\mathscr{P}(\lambda)$, if there is a regular uncountable cardinal $k \leq \lambda$ such that $\{x \in S: x \cap k \in k\}$ is stationary, then S can be split into $k$ disjoint stationary subsets.

Citation

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Toshimichi Usuba. "Splitting stationary sets in $\mathscr{P}(\lambda)$." J. Symbolic Logic 77 (1) 49 - 62, March 2012. https://doi.org/10.2178/jsl/1327068691

Information

Published: March 2012
First available in Project Euclid: 20 January 2012

zbMATH: 1250.03077
MathSciNet: MR2951629
Digital Object Identifier: 10.2178/jsl/1327068691

Subjects:
Primary: Primary 03E05; Secondary 03E55

Keywords: pcf-theory , saturated ideal , stationary set

Rights: Copyright © 2012 Association for Symbolic Logic

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Vol.77 • No. 1 • March 2012
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