{
  "id": "1412.4439",
  "version": "v1",
  "published": "2014-12-15T01:17:57.000Z",
  "updated": "2014-12-15T01:17:57.000Z",
  "title": "On Elementary Theories of GLP-Algebras",
  "authors": [
    "Fedor Pakhomov"
  ],
  "comment": "39 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "There is a polymodal provability logic $GLP$. We consider generalizations of this logic: the logics $GLP_{\\alpha}$, where $\\alpha$ ranges over linear ordered sets and play the role of the set of indexes of modalities. We consider the varieties of modal algebras that corresponds to the polymodal logics. We prove that the elementary theories of the free $\\emptyset$-generated $GLP_{n}$ -algebras are decidable for all finite ordinals $n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-15T01:17:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03F45",
      "03B25",
      "F.4.1"
    ],
    "keywords": [
      "elementary theories",
      "glp-algebras",
      "polymodal provability logic",
      "linear ordered sets",
      "modal algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.4439P"
    }
  }
}