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Reflecting stationary sets1

Published online by Cambridge University Press:  12 March 2014

Menachem Magidor
Menachem Magidor*
Affiliation:
The Hebrew University, Jerusalem, Israel
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Abstract

We prove that the statement “For every pair A, B, stationary subsets of ω2, composed of points of cofinality ω, there exists an ordinal α such that both A ∩ α and B ∩ α are stationary subsets of α is equiconsistent with the existence of weakly compact cardinal. (This completes results of Baumgartner and Harrington and Shelah.)

We also prove, assuming the existence of infinitely many supercompact cardinals, the statement “Every stationary subset of ωω+1 has a stationary initial segment.”

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 47 , Issue 4 , December 1982 , pp. 755 - 771
Copyright
Copyright © Association for Symbolic Logic 1982

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Footnotes

1

The author is grateful to Saharon Shelah for many helpful discussions concerning this paper.

References

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