2003/01/03 by Arthur W. Apter, Joel David Hamkins, Apter, Arthur W. +1
Computer Science · Mathematics · #03E35 #03E55 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis #math.LO #msc:03E35 #msc:03E55
paper · pdf · doi:10.48550/arxiv.math/0301016
30 pages. To appear in the Journal of Symbolic Logic
arxiv created 2003/01/03 · openalex publication_date 2003/01/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.