Indestructible Strong Compactness and Level by Level Equivalence with No Large Cardinal Restrictions

• Autorzy: Apter A. W.

Identyfikatory

DOI

10.4064/ba8014-12-2015

• Języki publikacji: EN

Abstrakty

EN

We construct a model for the level by level equivalence between strong compactness and supercompactness with an arbitrary large cardinal structure in which the least supercompact cardinal κ has its strong compactness indestructible under κ-directed closed forcing. This is in analogy to and generalizes the author’s result in Arch. Math. Logic 46 (2007), but without the restriction that no cardinal is supercompact up to an inaccessible cardinal.

Słowa kluczowe

EN

supercompact cardinal; strongly compact cardinal; indestructibility; Gitik iteration; Magidor iteration of Prikry forcing; level by level equivalence between strong compactness and supercompactness

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2015
• Tom: Vol. 63, no. 3
• Strony: 185--194
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Apter A. W.

• Department of Mathematics, Baruch College of CUNY, New York, NY 10010, U.S.A.
• The CUNY Graduate Center, Mathematics, 365 Fifth Avenue, New York, NY 10016, U.S.A.

Bibliografia

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• [3] A. Apter, Singular failures of GCH and level by level equivalence, Bull. Polish Acad. Sci. Math. 62 (2014), 11–21.
• [4] A. Apter, Supercompactness and level by level equivalence are compatible with indestructibility for strong compactness, Arch. Math. Logic 46 (2007), 155–163.
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• [6] A. Apter and J. Cummings, Identity crises and strong compactness II: strong cardinals, Arch. Math. Logic 40 (2001), 25–38.
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