Abstract
We prove from suitable large cardinal hypotheses that the least weakly compact cardinal can be unfoldable, weakly measurable and even nearly \({\theta}\)-supercompact, for any desired \({\theta}\). 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 \({\theta_\kappa}\)-supercompact cardinals \({\kappa}\), for nearly any desired function \({\kappa\mapsto\theta_\kappa}\). 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.
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The research of the second author was partially supported by Israel Science Foundation Grant No. 234/08 and 58/14. The research of the third author has been supported in part by NSF Grant DMS-0800762, PSC-CUNY Grant 64732-00-42 and Simons Foundation Grant 209252. Commentary concerning this paper can be made at http://jdh.hamkins.org/least-weakly-compact.
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Cody, B., Gitik, M., Hamkins, J.D. et al. The least weakly compact cardinal can be unfoldable, weakly measurable and nearly \({\theta}\)-supercompact. Arch. Math. Logic 54, 491–510 (2015). https://doi.org/10.1007/s00153-015-0423-1
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DOI: https://doi.org/10.1007/s00153-015-0423-1