{
  "id": "1807.07102",
  "version": "v1",
  "published": "2018-07-18T18:52:58.000Z",
  "updated": "2018-07-18T18:52:58.000Z",
  "title": "NIP omega-categorical structures: the rank 1 case",
  "authors": [
    "Pierre Simon"
  ],
  "comment": "52 pages",
  "categories": [
    "math.LO",
    "math.CO"
  ],
  "abstract": "We classify primitive, rank 1, omega-categorical structures having polynomially many types over finite sets, or equivalently at most exponential growth of the number of finite substructures. For a fixed number of 4-types, we show that there are only finitely many such structures and that all are built out of finitely many linear orders interacting in a restricted number of ways. As an example of application, we deduce the classification of primitive structures homogeneous in a language consisting of n linear orders as well as all reducts of such structures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-18T18:52:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C15",
      "03C64",
      "03C68",
      "06A05"
    ],
    "keywords": [
      "nip omega-categorical structures",
      "finite sets",
      "finite substructures",
      "exponential growth",
      "restricted number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 52,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}