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

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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DOI 10.2307/2273097
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References found in this work BETA

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 Pure and Applied 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 Pure and Applied Logic 4 (3):229.
Boolean Extensions and Measurable Cardinals.K. Kunen - 1971 - Annals of Pure and Applied Logic 2 (4):359.

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Citations of this work BETA

Squares, Scales and Stationary Reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (01):35-98.
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Simultaneous Stationary Reflection and Square Sequences.Yair Hayut & Chris Lambie-Hanson - 2017 - Journal of Mathematical Logic 17 (2):1750010.
A Model of Cummings and Foreman Revisited.Spencer Unger - 2014 - Annals of Pure and Applied Logic 165 (12):1813-1831.

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