Mixed Levels of Indestructibility

• Autorzy: Apter A. W.

Identyfikatory

DOI

10.4064/ba63-2-2

• Języki publikacji: EN

Abstrakty

EN

Starting from a supercompact cardinal κ, we force and construct a model in which κ is both the least strongly compact and least supercompact cardinal and κ exhibits mixed levels of indestructibility. Specifically, κ's strong compactness, but not its supercompactness, is indestructible under any κ-directed closed forcing which also adds a Cohen subset of κ. On the other hand, in this model, κ's supercompactness is indestructible under any κ-directed closed forcing which does not add a Cohen subset of κ.

Słowa kluczowe

EN

supercompact cardinal; strongly compact cardinal; strong cardinal; indestructibility; Prikry forcing; Prikry sequence; non-reflecting stationary set of ordinals; lottery sum

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2015
• Tom: Vol. 63, no. 2
• Strony: 113--122
• Opis fizyczny: Bibliogr. 13 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, M. Gitik and G. Sargsyan, Indestructible strong compactness but not supercompactness, Ann. Pure Appl. Logic 163 (2012), 1237–1242.
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• [6] J. D. Hamkins, Extensions with the approximation and cover properties have no new large cardinals, Fund. Math. 180 (2003), 257–277.
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• [8] J. D. Hamkins, Gap forcing: generalizing the Lévy–Solovay theorem, Bull. Symbolic Logic 5 (1999), 264–272.
• [9] J. D. Hamkins, The lottery preparation, Ann. Pure Appl. Logic 101 (2000), 103–146.
• [10] T. Jech, Set Theory. The Third Millennium Edition, Revised and Expanded, Springer, Berlin, 2003.
• [11] R. Laver, Making the supercompactness of κ indestructible under κ-directed closed forcing, Israel J. Math. 29 (1978), 385–388.
• [12] M. Magidor, How large is the first strongly compact cardinal? or A study on identity crises, Ann. Math. Logic 10 (1976), 33–57.
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