{
  "id": "1610.09660",
  "version": "v1",
  "published": "2016-10-30T15:23:49.000Z",
  "updated": "2016-10-30T15:23:49.000Z",
  "title": "Canonical Functions: a proof via topological dynamics",
  "authors": [
    "Manuel Bodirsky",
    "Michael Pinsker"
  ],
  "comment": "7 pages",
  "categories": [
    "math.CO",
    "cs.CC",
    "math.DS",
    "math.LO"
  ],
  "abstract": "Canonical functions are a powerful concept with numerous applications in the study of groups, monoids, and clones on countable structures with Ramsey-type properties. In this short note, we present a proof of the existence of canonical functions in certain sets using topological dynamics, providing a shorter alternative to the original combinatorial argument. We moreover present equivalent algebraic characterisations of canonicity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-30T15:23:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "canonical functions",
      "topological dynamics",
      "original combinatorial argument",
      "equivalent algebraic characterisations",
      "ramsey-type properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}