{
  "id": "2302.01609",
  "version": "v1",
  "published": "2023-02-03T09:15:14.000Z",
  "updated": "2023-02-03T09:15:14.000Z",
  "title": "Embedding the prime model of real exponentiation into o-minimal exponential fields",
  "authors": [
    "Lothar Sebastian Krapp"
  ],
  "comment": "11 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "Motivated by the decidability question for the theory of real exponentiation and by the Transfer Conjecture for o-minimal exponential fields, we show that, under the assumption of Schanuel's Conjecture, the prime model of real exponentiation is embeddable into any o-minimal exponential field. This is deduced from a more general unconditional result on the embeddability of exponential algebraic closures in o-minimal exponential fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-03T09:15:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C64",
      "03C60",
      "12J15",
      "12L12",
      "12J10"
    ],
    "keywords": [
      "o-minimal exponential field",
      "real exponentiation",
      "prime model",
      "exponential algebraic closures",
      "general unconditional result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}