{
  "id": "2203.06156",
  "version": "v1",
  "published": "2022-03-11T18:31:18.000Z",
  "updated": "2022-03-11T18:31:18.000Z",
  "title": "Hindman's Theorem in the hierarchy of Choice Principles",
  "authors": [
    "David J. Fernández-Bretón"
  ],
  "comment": "17 pages, 2 figures",
  "categories": [
    "math.LO"
  ],
  "abstract": "In the context of $\\mathsf{ZF}$, we analyze a version of Hindman's finite unions theorem on infinite sets, which normally requires the Axiom of Choice to be proved. We establish the implication relations between this statement and various classical weak choice principles, thus precisely locating the strength of the statement as a weak form of the $\\mathsf{AC}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-11T18:31:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E25",
      "03E35",
      "03E30",
      "03E65",
      "03E02",
      "03E05"
    ],
    "keywords": [
      "hindmans theorem",
      "hindmans finite unions theorem",
      "classical weak choice principles",
      "weak form",
      "infinite sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}