The least weakly compact cardinal can be unfoldable, weakly measurable and nearly θ-supercompact

Brent Cody*, Moti Gitik, Joel David Hamkins, Jason A. Schanker

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We prove from suitable large cardinal hypotheses that the least weakly compact cardinal can be unfoldable, weakly measurable and even nearly θ-supercompact, for any desired θ. In addition, we prove several global results showing how the entire class of weakly compactcardinals, a proper class, can be made to coincide with the class of unfoldable cardinals, with the class of weakly measurable cardinals or with the class of nearly θκ-supercompact cardinals κ, for nearly any desired function κ↦θκ. These results answer several questions that had been open in the literature and extend to these large cardinals the identity-crises phenomenon, first identified by Magidor with the strongly compact cardinals.

Original languageEnglish
Pages (from-to)491-510
Number of pages20
JournalArchive for Mathematical Logic
Volume54
Issue number5-6
DOIs
StatePublished - 27 Aug 2015

Funding

FundersFunder number
National Science Foundation
PSC-CUNY64732-00-42
National Science FoundationDMS-0800762
Simons Foundation209252
Israel Science Foundation58/14, 234/08

    Keywords

    • Identity crisis
    • Nearly supercompact
    • Unfoldable
    • Weakly compact
    • Weakly measurable

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