{
  "id": "2002.12929",
  "version": "v1",
  "published": "2020-02-28T18:56:11.000Z",
  "updated": "2020-02-28T18:56:11.000Z",
  "title": "On coincidence of dimensions in closed ordered differential fields",
  "authors": [
    "Pantelis E. Eleftheriou",
    "Omar Leon Sanchez",
    "Nathalie Regnault"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "Let $(R, \\delta)$ be a closed ordered differential field, and $C$ its field of constants. In this note, we prove that for sets definable in the pair $(R, C)$, the $\\delta$-dimension and the large dimension coincide. As an application, we characterize the definable sets that are internal to $C$, as those sets that are definable in $(R, C)$ and have $\\delta$-dimension $0$. We further show that having $\\delta$-dimension $0$ does not generally imply co-analyzability in $C$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-28T18:56:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C98",
      "03C60"
    ],
    "keywords": [
      "closed ordered differential field",
      "coincidence",
      "large dimension coincide",
      "application",
      "definable sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}