Journal of Symbolic Logic

Reflecting Stationary Sets

Menachem Magidor

Abstract

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."

Article information

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

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183741137

Mathematical Reviews number (MathSciNet)
MR683153

Zentralblatt MATH identifier
0506.03014

JSTOR