Exactly controlling the non-supercompact strongly compact cardinals

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dc.creatorApter, Arthur W.
dc.creatorHamkins, Joel David
dc.date2003-01-03
dc.date.accessioned2026-07-07T04:54:14Z
dc.date.available2026-07-07T04:54:14Z
dc.descriptionWe 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.
dc.description30 pages. To appear in the Journal of Symbolic Logic
dc.identifierhttps://arxiv.org/abs/math/0301016
dc.identifierhttp://arxiv.org/abs/math/0301016
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/66171
dc.subjectLogic
dc.subject03E35; 03E55
dc.titleExactly controlling the non-supercompact strongly compact cardinals
dc.typetext

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