{
  "id": "2310.09451",
  "version": "v1",
  "published": "2023-10-13T23:58:55.000Z",
  "updated": "2023-10-13T23:58:55.000Z",
  "title": "First-order model theory and Kaplansky's stable finiteness conjecture",
  "authors": [
    "Tullio Ceccherini-Silberstein",
    "Michel Coornaert",
    "Xuan Kien Phung"
  ],
  "categories": [
    "math.GR",
    "math.LO",
    "math.RA"
  ],
  "abstract": "Using algebraic geometry methods, the third author proved that the group ring of a surjunctive group with coefficients in a field is always stably finite. In other words, every group satisfying Gottschalk's conjecture also satisfies Kaplansky's stable finiteness conjecture. Here we present an alternative proof of this result based on first-order model theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-13T23:58:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C98",
      "20E07",
      "37B15",
      "14A10",
      "68Q80"
    ],
    "keywords": [
      "first-order model theory",
      "satisfies kaplanskys stable finiteness conjecture",
      "algebraic geometry methods",
      "group satisfying gottschalks conjecture",
      "third author"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}