{
  "id": "1609.07694",
  "version": "v1",
  "published": "2016-09-25T02:45:11.000Z",
  "updated": "2016-09-25T02:45:11.000Z",
  "title": "Infinitely many reducts of homogeneous structures",
  "authors": [
    "Bertalan Bodor",
    "Peter J. Cameron",
    "Csaba Szabó"
  ],
  "comment": "Submitted to Algebra Universalis",
  "categories": [
    "math.LO",
    "math.GR"
  ],
  "abstract": "It is shown that the countably infinite dimensional pointed vector space (the vector space equipped with a constant) over a finite field has infinitely many first order definable reducts. This implies that the countable homogeneous Boolean-algebra has infinitely many reducts. Our construction over the 2-element field is related to the Reed--Muller codes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-25T02:45:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C15"
    ],
    "keywords": [
      "homogeneous structures",
      "infinite dimensional pointed vector space",
      "countably infinite dimensional pointed vector",
      "first order definable reducts",
      "reed-muller codes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}