Exactly controlling the non-supercompact strongly compact cardinals [article]

Arthur W. Apter, Joel David Hamkins
2003 arXiv   pre-print
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
more » ... f measurable cardinals. These results improve and unify previous results of the first author.
arXiv:math/0301016v1 fatcat:znxl2yyz4vcpjjzwbmyjvysrfm