{
  "id": "1104.4606",
  "version": "v1",
  "published": "2011-04-24T06:22:32.000Z",
  "updated": "2011-04-24T06:22:32.000Z",
  "title": "Universal Algebra and Mathematical Logic",
  "authors": [
    "Zhaohua Luo"
  ],
  "categories": [
    "math.LO",
    "cs.FL",
    "cs.LO"
  ],
  "abstract": "In this paper, first-order logic is interpreted in the framework of universal algebra, using the clone theory developed in three previous papers. We first define the free clone T(L, C) of terms of a first order language L over a set C of parameters in a standard way. The free right algebra F(L, C) of formulas over T(L, C) is then generated by atomic formulas. Structures for L over C are represented as perfect valuations of F(L, C), and theories of L are represented as filters of F(L). Finally Godel's completeness theorem and first incompleteness theorem are stated as expected.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-24T06:22:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "universal algebra",
      "mathematical logic",
      "first incompleteness theorem",
      "godels completeness theorem",
      "first order language"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.4606L"
    }
  }
}