{
  "id": "1407.6335",
  "version": "v2",
  "published": "2014-07-23T19:15:41.000Z",
  "updated": "2015-07-03T19:17:16.000Z",
  "title": "Large cardinals need not be large in HOD",
  "authors": [
    "Yong Cheng",
    "Sy-David Friedman",
    "Joel David Hamkins"
  ],
  "comment": "20 pages. Commentary concerning this article can be made at http://jdh.hamkins.org/large-cardinals-need-not-be-large-in-hod",
  "categories": [
    "math.LO"
  ],
  "abstract": "We prove that large cardinals need not generally exhibit their large cardinal nature in HOD. For example, a supercompact cardinal $\\kappa$ need not be weakly compact in HOD, and there can be a proper class of supercompact cardinals in $V$, none of them weakly compact in HOD, with no supercompact cardinals in HOD. Similar results hold for many other types of large cardinals, such as measurable and strong cardinals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-23T19:15:41.000Z",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-07-03T19:17:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E55",
      "03E45"
    ],
    "keywords": [
      "large cardinals",
      "supercompact cardinal",
      "similar results hold",
      "large cardinal nature",
      "weakly compact"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.6335C"
    }
  }
}