On a problem of Foreman and Magidor

Abstract

A question of Foreman and Magidor asks if it is consistent for every sequence of stationary subsets of the ℵn’s for 1≤n<ω to be mutually stationary. We get a positive answer to this question in the context of the negation of the Axiom of Choice. We also indicate how a positive answer to a generalized version of this question in a choiceless context may be obtained.