Universal indestructibility is consistent with two strongly compact cardinals

• Autorzy: Apter A. W.

Identyfikatory

DOI

10.4064/ba53-2-2

• Języki publikacji: EN

Abstrakty

EN

We show that universal indestructibility for both strong compactness and supercompactness is consistent with the existence of two strongly compact cardinals. This is in contrast to the fact that if κ is supercompact and universal indestructibility for either strong compactness or supercompactness holds, then no cardinal λ > κ is measurable.

Słowa kluczowe

EN

supercompact cardinal; strongly compact cardinal; indestructibility; universal indestructibility

PL

niezniszczalność; niezniszczalność uniwersalna

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2005
• Tom: Vol. 53, no 2
• Strony: 131--135
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Apter A. W.

• Department of Mathematics, Baruch College of CUNY, New York, NY 10010, U.S.A.

Bibliografia

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• [7] R. Laver, Making the supercompactness of κ indestructible under к-directed closed forcing, Israel J. Math. 29 (1978), 385—388.
• [8] A. Lévy and R. Solovay, Measurable cardinals and the continuum hypothesis, ibid. 5 (1967), 234-248.
• [9] R. Solovay, Strongly compact cardinals and the GCH, in: Proceedings of the Tarski Symposium, Proc. Sympos. Pure Math. 25, Amer. Math. Soc., Providence, 1974, 365-372.
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