{
  "id": "1609.03722",
  "version": "v1",
  "published": "2016-09-13T08:26:21.000Z",
  "updated": "2016-09-13T08:26:21.000Z",
  "title": "On the local closure of clones on countable sets",
  "authors": [
    "Erhard Aichinger"
  ],
  "categories": [
    "math.LO",
    "math.RA"
  ],
  "abstract": "We consider clones on countable sets. If such a clone has quasigroup operations, is locally closed and countable, then there is a function $f : \\mathbb{N} \\to \\mathbb{N}$ such that the $n$-ary part of $C$ is equal to the $n$-ary part of $\\mathrm{Pol}\\,\\mathrm{Inv}^{[f(n)]} C$, where $\\mathrm{Inv}^{[f(n)]} C$ denotes the set of $f(n)$-ary invariant relations of $C$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-13T08:26:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "08A40"
    ],
    "keywords": [
      "countable sets",
      "local closure",
      "ary part",
      "ary invariant relations",
      "quasigroup operations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}