{
  "id": "2008.01770",
  "version": "v1",
  "published": "2020-08-04T19:13:15.000Z",
  "updated": "2020-08-04T19:13:15.000Z",
  "title": "The domination monoid in o-minimal theories",
  "authors": [
    "Rosario Mennuni"
  ],
  "comment": "31 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We study the monoid of global invariant types modulo domination-equivalence in the context of o-minimal theories. We reduce its computation to the problem of proving that it is generated by classes of 1-types. We show this to hold in Real Closed Fields, where generators of this monoid correspond to invariant convex subrings of the monster model. Combined with arxiv:1702.06504, this allows us to compute the domination monoid in the weakly o-minimal theory of Real Closed Valued Fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-04T19:13:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C45",
      "03C64",
      "03C60",
      "12J10"
    ],
    "keywords": [
      "o-minimal theory",
      "domination monoid",
      "global invariant types modulo domination-equivalence",
      "invariant convex subrings",
      "real closed fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}