Reflecting stationary sets

Journal of Symbolic Logic 47 (4):755-771 (1982)
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Abstract

We prove that the statement "For every pair A, B, stationary subsets of ω 2 , composed of points of cofinality ω, there exists an ordinal α such that both A ∩ α and $B \bigcap \alpha$ 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 ω ω + 1 has a stationary initial segment."

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References found in this work

Set Theory.Keith J. Devlin - 1981 - Journal of Symbolic Logic 46 (4):876-877.
Strong axioms of infinity and elementary embeddings.Robert M. Solovay - 1978 - Annals of Mathematical Logic 13 (1):73.
A new class of order types.James E. Baumgartner - 1976 - Annals of Mathematical Logic 9 (3):187-222.
The fine structure of the constructible hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.
Boolean extensions and measurable cardinals.K. Kunen - 1971 - Annals of Mathematical Logic 2 (4):359.

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