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## Bulletin of the Polish Academy of Sciences. Mathematics

2008 | 56 | 3 | 191-197
Tytuł artykułu

### A Note on Indestructibility and Strong Compactness

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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.
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Tom
Numer
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191-197
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wydano
2008
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autor
• 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.
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