Exactly controlling the non-supercompact strongly compact cardinals

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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 previous results of the first author.
30 pages. To appear in the Journal of Symbolic Logic

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Logic, 03E35; 03E55

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http://salesiana.dossiersoluciones.com/handle/123456789/66171

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0301016
 http://arxiv.org/abs/math/0301016

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arXiv