{
  "id": "1112.4189",
  "version": "v1",
  "published": "2011-12-18T21:05:45.000Z",
  "updated": "2011-12-18T21:05:45.000Z",
  "title": "Comparison of Exponential-Logarithmic and Logarithmic-Exponential series",
  "authors": [
    "Marcus Tressl",
    "Salma Kuhlmann"
  ],
  "journal": "Math. Logic Quarterly, 58, No. 6, 434 - 448 (2012)",
  "categories": [
    "math.LO",
    "math.AC"
  ],
  "abstract": "We explain how the field of logarithmic-exponential series constructed in \\cite{DMM1} and \\cite {DMM2} embeds as an exponential field in any field of exponential-logarithmic series constructed in \\cite{KK1}, \\cite {K} and \\cite {KS}. On the other hand, we explain why no field of exponential-logarithmic series embeds in the field of logarithmic-exponential series. This clarifies why the two constructions are intrinsically different, in the sense that they produce non-isomorphic models of Th$(\\R_{an, exp})$; the elementary theory of the ordered field of real numbers, with the exponential function and restricted analytic functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-12-18T21:05:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "logarithmic-exponential series",
      "comparison",
      "exponential-logarithmic series embeds",
      "produce non-isomorphic models",
      "exponential field"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.4189T"
    }
  }
}