A Note on Indestructibility and Strong Compactness

• Autorzy: Arthur W. Apter
• Języki publikacji: EN

Abstrakty

EN

If κ < λ are such that κ is both supercompact and indestructible under κ-directed closed forcing which is also (κ⁺,∞)-distributive and λ is $2^λ$ supercompact, then by a result of Apter and Hamkins [J. Symbolic Logic 67 (2002)], {δ < κ | δ is δ⁺ strongly compact yet δ is not δ⁺ supercompact} must be unbounded in κ. We show that the large cardinal hypothesis on λ is necessary by constructing a model containing a supercompact cardinal κ in which no cardinal δ > κ is $2^δ = δ⁺$ supercompact, κ's supercompactness is indestructible under κ-directed closed forcing which is also (κ⁺,∞)-distributive, and for every measurable cardinal δ, δ is δ⁺ strongly compact iff δ is δ⁺ supercompact.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2008
• Tom: 56
• Numer: 3
• Strony: 191-197

Daty

wydano

2008

Twórcy

autor

Arthur W. Apter

• 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.

Identyfikatory

DOI

10.4064/ba56-3-1