{
  "id": "1803.03153",
  "version": "v1",
  "published": "2018-03-08T15:31:50.000Z",
  "updated": "2018-03-08T15:31:50.000Z",
  "title": "Value Groups and Residue Fields of Models of Real Exponentiation",
  "authors": [
    "Lothar Sebastian Krapp"
  ],
  "comment": "28 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "Let $F$ be an archimedean field, $G$ a divisible ordered abelian group and $h$ a group exponential on $G$. A triple $(F,G,h)$ is realised in a non-archimedean exponential field $(K,\\exp)$ if the residue field of $K$ under the natural valuation is $F$ and the induced exponential group of $(K,\\exp)$ is $(G,h)$. We give a full characterisation of all triples $(F,G,h)$ which can be realised in a model of real exponentiation in the following two cases: i) $G$ is countable. ii) $G$ is $\\kappa$-saturated for an uncountable regular cardinal $\\kappa$ with $\\kappa^{<\\kappa} = \\kappa$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-08T15:31:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "residue field",
      "real exponentiation",
      "value groups",
      "non-archimedean exponential field",
      "full characterisation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}