{
  "id": "2004.10953",
  "version": "v1",
  "published": "2020-04-23T03:07:58.000Z",
  "updated": "2020-04-23T03:07:58.000Z",
  "title": "Stable formulas in ordered structures",
  "authors": [
    "Daniel Max Hoffmann",
    "Chieu-Minh Tran",
    "Jinhe Ye"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We classify the stable formulas in the theory of Dense Linear Orders without endpoints, the stable formulas in the theory of Divisible Abelian Groups, and the stable formulas without parameters in the theory of Real Closed Fields. The third result, unexpectedly, requires the Hironaka's theorem on resolution of singularities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-23T03:07:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C64",
      "03C45",
      "03C10"
    ],
    "keywords": [
      "stable formulas",
      "ordered structures",
      "dense linear orders",
      "divisible abelian groups",
      "hironakas theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}