Identity crises and strong compactness

Journal of Symbolic Logic 65 (4):1895-1910 (2000)
Abstract
Combining 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 κ 1 ,..., κ n are so that κ i for i = 1,..., n is both the i th measurable cardinal and κ + i supercompact. This generalizes an unpublished theorem of Magidor and answers a question of Apter and Shelah
Keywords Strongly Compact Cardinal   Supercompact Cardinal   Measurable Cardinal   Identity Crisis   Reverse Easton Iteration
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Joel D. Hamkins (2009). Tall Cardinals. Mathematical Logic Quarterly 55 (1):68-86.
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