{
  "id": "2208.09380",
  "version": "v1",
  "published": "2022-08-19T14:50:57.000Z",
  "updated": "2022-08-19T14:50:57.000Z",
  "title": "On compactness of weak square at singulars of uncountable cofinality",
  "authors": [
    "Maxwell Levine"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "Cummings, Foreman, and Magidor proved that Jensen's square principle is non-compact at $\\aleph_\\omega$, meaning that it is consistent that $\\square_{\\aleph_n}$ holds for all $n<\\omega$ while $\\square_{\\aleph_\\omega}$ fails. We investigate the natural question of whether this phenomenon generalizes to singulars of uncountable cofinality. Surprisingly, we show that under some mild hypotheses, the weak square principle $\\square_\\kappa^*$ is in fact compact at singulars of uncountable cofinality, and that an even stronger version of these hypotheses is not enough for compactness of weak square at $\\aleph_\\omega$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-19T14:50:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E04",
      "03E35",
      "03E55"
    ],
    "keywords": [
      "uncountable cofinality",
      "compactness",
      "jensens square principle",
      "weak square principle",
      "natural question"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}