Exactly controlling the non-supercompact strongly compact cardinals
release_szzk73eqxvbllne3j6v2notbpy
by
Arthur W. Apter, Joel David Hamkins
2003 Volume 68, Issue 02, p669-688
Abstract
<jats:title>Abstract</jats:title>
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 [5], due to the first author.
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