{
  "id": "2308.13942",
  "version": "v1",
  "published": "2023-08-26T19:13:05.000Z",
  "updated": "2023-08-26T19:13:05.000Z",
  "title": "When does $\\aleph_1$-categoricity imply $ω$-stability?",
  "authors": [
    "John T. Baldwin",
    "M. C. Laskowski",
    "Saharon Shelah"
  ],
  "comment": "22 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "For an $\\aleph_1$-categorical atomic class, we clarify the space of types over the unique model of size $\\aleph_1$. Using these results, we prove that if such a class has a model of size $\\beth_1^+$ then it is $\\omega$-stable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-26T19:13:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C45"
    ],
    "keywords": [
      "categoricity",
      "categorical atomic class",
      "unique model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}