{
  "id": "1607.07173",
  "version": "v1",
  "published": "2016-07-25T08:02:57.000Z",
  "updated": "2016-07-25T08:02:57.000Z",
  "title": "Dimension in the realm of transseries",
  "authors": [
    "Matthias Aschenbrenner",
    "Lou van den Dries",
    "Joris van der Hoeven"
  ],
  "comment": "16 pp",
  "categories": [
    "math.LO",
    "math.CA"
  ],
  "abstract": "Let $\\mathbb T$ be the differential field of transseries. We establish some basic properties of the dimension of a definable subset of ${\\mathbb T}^n$, also in relation to its codimension in the ambient space ${\\mathbb T}^n$. The case of dimension $0$ is of special interest, and can be characterized both in topological terms (discreteness) and in terms of the Herwig-Hrushovski-Macpherson notion of co-analyzability. The proofs use results by the authors from \"Asymptotic Differential Algebra and Model Theory of Transseries\", the axiomatic framework for \"dimension\" in [L. van den Dries, \"Dimension of definable sets, algebraic boundedness and Henselian fields\", Ann. Pure Appl. Logic 45 (1989), no. 2, 189-209], and facts about co-analyzability from [B. Herwig, E. Hrushovski, D. Macpherson, \"Interpretable groups, stably embedded sets, and Vaughtian pairs\", J. London Math. Soc. (2003) 68, no. 1, 1-11].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-25T08:02:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "transseries",
      "asymptotic differential algebra",
      "van den dries",
      "basic properties",
      "ambient space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}