{
  "id": "2212.13605",
  "version": "v1",
  "published": "2022-12-27T20:30:21.000Z",
  "updated": "2022-12-27T20:30:21.000Z",
  "title": "Vaught's conjecture for theories of discretely ordered structures",
  "authors": [
    "Predrag Tanović"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "Let $T$ be a countable complete first-order theory with a definable, infinite, discrete linear order. We prove that $T$ has continuum-many countable models. The proof is purely first-order, but raises the question of Borel completeness of $T$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-27T20:30:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C15",
      "03C45"
    ],
    "keywords": [
      "discretely ordered structures",
      "vaughts conjecture",
      "countable complete first-order theory",
      "discrete linear order",
      "borel completeness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}