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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 This generalizes an unpublished theorem of Magidor and answers a question of Apter and Shelah.Other Versions
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Citations of this work
On Restrictions of Ultrafilters From Generic Extensions to Ground Models.Moti Gitik & Eyal Kaplan - 2023 - Journal of Symbolic Logic 88 (1):169-190.
Exactly controlling the non-supercompact strongly compact cardinals.Arthur W. Apter & Joel David Hamkins - 2003 - Journal of Symbolic Logic 68 (2):669-688.
Indestructibility and level by level equivalence and inequivalence.Arthur W. Apter - 2007 - Mathematical Logic Quarterly 53 (1):78-85.
Level by level inequivalence beyond measurability.Arthur W. Apter - 2011 - Archive for Mathematical Logic 50 (7-8):707-712.
References found in this work
Strong axioms of infinity and elementary embeddings.Robert M. Solovay - 1978 - Annals of Mathematical Logic 13 (1):73.
On strong compactness and supercompactness.Telis K. Menas - 1975 - Annals of Mathematical Logic 7 (4):327-359.
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.
Laver Indestructibility and the Class of Compact Cardinals.Arthur W. Apter - 1998 - Journal of Symbolic Logic 63 (1):149-157.
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