Identity crises and strong compactness

Abstract

AbstractCombining techniques of the first author and Shelah with ideas of Magidor, we show how to get a model in which, for fixed but arbitrary finite n, the first n strongly compact cardinals k1..…kn are so that ki; for i = 1..…n is both the ith measurable cardinal and supercompact. This generalizes an unpublished theorem of Magidor and answers a question of Apter and Shelah.