A reduction in consistency strength for universal indestructibility

• Autorzy: Apter A. W. , Sargsyan G.
• Języki publikacji: EN

Abstrakty

EN

We show how to reduce the assumptions in consistency strength used to prove several theorems on universal indestructibility.

Słowa kluczowe

EN

universal indestructibility; indestructibility; measurable cardinal; Woodin cardinal; strongly compact cardinal; supercompact cardinal; cardinal Woodin for supercompactness; high-jump cardinal; almost huge cardinal

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2007
• Tom: Vol. 55, no 1
• Strony: 1--6
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Apter A. W.

autor

Sargsyan G.

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

Bibliografia

• [1] A. Apter, Universal indestructibility is consistent with two strongly compact cardinals, Bull. Polish Acad. Sci. Math. 53 (2005), 131-135.
• [2] A. Apter and M. Gitik, The least measurable can be strongly compact and indestructible, J. Symbolic Logic 63 (1998), 1404-1412.
• [3] A. Apter and J. D. Hamkins, Universal indestructibility, Kobe J. Math. 16 (1999), 119-130.
• [4] J. D. Hamkins, Gap forcing, Israel J. Math. 125 (2001), 237-252.
• [5] —, Gap forcing: generalizing the Levy-Solovay theorem, Bull. Symbolic Logic 5 (1999), 264-272.
• [6] A. Kanamori, The Higher Infinite, Springer, Berlin, 1994.
• [7] R. Laver, Making the supercompactness of Κ indestructible under κ-directed closed forcing, Israel J. Math. 29 (1978), 385-388.
• [8] A. Levy and R. Solovay, Measurable cardinals and the continuum hypothesis, ibid. 5 (1967), 234-248.