Indestructible strong compactness but not supercompactness

Arthur W. Apter, Moti Gitik, Grigor Sargsyan

Research output: Contribution to journalArticlepeer-review


Starting from a supercompact cardinal κ, we force and construct a model in which κ is both the least strongly compact and least supercompact cardinal and κ's strong compactness, but not its supercompactness, is indestructible under arbitrary κ-directed closed forcing.

Original languageEnglish
Pages (from-to)1237-1242
Number of pages6
JournalAnnals of Pure and Applied Logic
Issue number9
StatePublished - Sep 2012


  • Indestructibility
  • Prikry forcing
  • Strongly compact
  • Supercompact


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