Journal of Symbolic Logic

Reflecting Stationary Sets

Menachem Magidor

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We prove that the statement "For every pair $A, B$, stationary subsets of $\omega_2$, composed of points of cofinality $\omega$, there exists an ordinal $\alpha$ such that both $A \cap \alpha$ and $B \bigcap \alpha$ are stationary subsets of $\alpha$" 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 $\omega_{\omega + 1}$ has a stationary initial segment."

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J. Symbolic Logic, Volume 47, Issue 4 (1982), 755-771.

First available in Project Euclid: 6 July 2007

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Magidor, Menachem. Reflecting Stationary Sets. J. Symbolic Logic 47 (1982), no. 4, 755--771.

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