Journal of Symbolic Logic 65 (4):1895-1910 (2000)
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 This generalizes an unpublished theorem of Magidor and answers a question of Apter and Shelah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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References found in this work BETA
Strong Axioms of Infinity and Elementary Embeddings.Robert M. Solovay, William N. Reinhardt & Akihiro Kanamori - 1978 - Annals of Mathematical Logic 13 (1):73-116.
How Large is the First Strongly Compact Cardinal? Or a Study on Identity Crises.Menachem Magidor - 1976 - Annals of Mathematical Logic 10 (1):33-57.
Patterns of Compact Cardinals.Arthur W. Apter - 1997 - Annals of Pure and Applied Logic 89 (2-3):101-115.
Some Results on Consecutive Large Cardinals.Arthur W. Apter - 1983 - Annals of Pure and Applied Logic 25 (1):1-17.
More on the Least Strongly Compact Cardinal.Arthur W. Apter - 1997 - Mathematical Logic Quarterly 43 (3):427-430.
Citations of this work BETA
Failures of SCH and Level by Level Equivalence.Arthur W. Apter - 2006 - Archive for Mathematical Logic 45 (7):831-838.
Supercompactness and Level by Level Equivalence Are Compatible with Indestructibility for Strong Compactness.Arthur W. Apter - 2007 - Archive for Mathematical Logic 46 (3-4):155-163.
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