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Apter, Arthur W.; Hamkins, Joel David

Exactly controlling the non-supercompact strongly compact cardinals. (English) Zbl 1056.03030

J. Symb. Log. 68, No. 2, 669-688 (2003).
Summary: We summarize the known methods of producing a non-supercompact strongly compact cardinal and describe some new variants. Our Main Theorem shows how to apply these methods to many cardinals simultaneously and exactly control which cardinals are supercompact and which are only strongly compact in a forcing extension. Depending upon the method, the surviving non-supercompact strongly compact cardinals can be strong cardinals, have trivial Mitchell rank or even contain a club disjoint from the set of measurable cardinals. These results improve and unify Theorems 1 and 2 of Ann. Pure Appl. Logic 89, 101–115 (1997; Zbl 0890.03026), due to the first author.

Cited in 7 Documents

MSC:

03E55 Large cardinals
03E35 Consistency and independence results

Keywords:

strongly compact cardinal; supercompact cardinal; strong cardinal; indestructibility; non-reflecting stationary set of ordinals

Citations:

Zbl 0890.03026
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Full Text: DOI arXiv Euclid

References:

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