{
  "id": "1910.11230",
  "version": "v1",
  "published": "2019-10-24T15:36:20.000Z",
  "updated": "2019-10-24T15:36:20.000Z",
  "title": "Counting siblings in universal theories",
  "authors": [
    "Samuel Braunfeld",
    "Michael C. Laskowski"
  ],
  "comment": "25 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We show that if a countable structure $M$ in a finite relational language is not cellular, then there is an age-preserving $N \\supseteq M$ such that $2^{\\aleph_0}$ many structures are bi-embeddable with $N$. The proof proceeds by a case division based on mutual algebraicity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-24T15:36:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C15"
    ],
    "keywords": [
      "universal theories",
      "counting siblings",
      "finite relational language",
      "case division",
      "proof proceeds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}