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Splitting stationary sets in

Published online by Cambridge University Press:  12 March 2014

Toshimichi Usuba
Toshimichi Usuba*
Affiliation:
Institute for Advanced Research, Nagoya University, Furo-Cho, Chikusa-Ku, Nagoya, 464-8601, Japan, E-mail: usuba@math.cm.is.nagoya-u.ac.jp
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Abstract

Let A be a non-empty set. A set is said to be stationary in if for every f: [A]<ω → A there exists x ϵ S such that x ≠ A and f“[x]<ω ⊆ x. In this paper we prove the following: For an uncountable cardinal λ and a stationary set S in , if there is a regular uncountable cardinal κ ≤ λ such that {x ϵ S: x ∩ κ ϵ κ} is stationary, then S can be split into κ disjoint stationary subsets.

Keywords

stationary setsaturated idealpcf-theory
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 1 , March 2012 , pp. 49 - 62
Copyright
Copyright © Association for Symbolic Logic 2012

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References

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