{
  "id": "1306.2669",
  "version": "v1",
  "published": "2013-06-11T22:09:21.000Z",
  "updated": "2013-06-11T22:09:21.000Z",
  "title": "Hilbert's Tenth Problem over Function Fields of Positive Characteristic Not Containing the Algebraic Closure of a Finite Field",
  "authors": [
    "Kirsten Eisentraeger",
    "Alexandra Shlapentokh"
  ],
  "categories": [
    "math.NT",
    "math.LO"
  ],
  "abstract": "We prove that the existential theory of any function field $K$ of characteristic $p> 0$ is undecidable in the language of rings provided that the constant field does not contain the algebraic closure of a finite field. We also extend the undecidability proof for function fields of higher transcendence degree to characteristic 2 and show that the first-order theory of {\\bf any} function field of positive characteristic is undecidable in the language of rings without parameters.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-11T22:09:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C07",
      "03D35",
      "11U05"
    ],
    "keywords": [
      "function field",
      "algebraic closure",
      "finite field",
      "positive characteristic",
      "higher transcendence degree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.2669E"
    }
  }
}