{
  "id": "1305.5961",
  "version": "v1",
  "published": "2013-05-25T19:35:26.000Z",
  "updated": "2013-05-25T19:35:26.000Z",
  "title": "The least weakly compact cardinal can be unfoldable, weakly measurable and nearly $θ$-supercompact",
  "authors": [
    "Brent Cody",
    "Moti Gitik",
    "Joel David Hamkins",
    "Jason Schanker"
  ],
  "comment": "25 pages. Commentary concerning this paper can be made at http://jdh.hamkins.org/least-weakly-compact",
  "categories": [
    "math.LO"
  ],
  "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 compact cardinals, 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-25T19:35:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weakly compact cardinal",
      "weakly measurable",
      "unfoldable",
      "suitable large cardinal hypotheses",
      "identity-crises phenomenon"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.5961C"
    }
  }
}