{
  "id": "2202.01623",
  "version": "v1",
  "published": "2022-02-03T14:51:47.000Z",
  "updated": "2022-02-03T14:51:47.000Z",
  "title": "On the cofinality of the least $λ$-strongly compact cardinal",
  "authors": [
    "Zhixing You",
    "Jiachen Yuan"
  ],
  "comment": "15 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "In this paper, we characterize the possible cofinalities of the least $\\lambda$-strongly compact cardinal. We show that, on the one hand, for any regular cardinal, $\\delta$, that carries a $\\lambda$-complete uniform ultrafilter, it is consistent, relative to the existence of a supercompact cardinal above $\\delta$, that the least $\\lambda$-strongly compact cardinal has cofinality $\\delta$. On the other hand, provably the cofinality of the least $\\lambda$-strongly compact cardinal always carries a $\\lambda$-complete uniform ultrafilter.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-03T14:51:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E35",
      "03E55"
    ],
    "keywords": [
      "strongly compact cardinal",
      "cofinality",
      "complete uniform ultrafilter",
      "regular cardinal",
      "supercompact cardinal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}