{
  "id": "1711.06160",
  "version": "v1",
  "published": "2017-11-16T15:57:35.000Z",
  "updated": "2017-11-16T15:57:35.000Z",
  "title": "The Class of Countable Projective Planes is Borel Complete",
  "authors": [
    "Gianluca Paolini"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We observe that Hall's free projective extension $P \\mapsto F(P)$ of partial planes is a Borel map, and use a modification of the construction introduced in [9] to conclude that the class of countable non-Desarguesian projective planes is Borel complete. In the process, we also rediscover the main result of [7] on the realizability of every group as the group of collineations of some projective plane. Finally, we use classical results of projective geometry to prove that the class of countable Pappian projective planes is Borel complete.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-16T15:57:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51A35",
      "03E15",
      "54H05",
      "05B35",
      "22F50"
    ],
    "keywords": [
      "borel complete",
      "countable projective planes",
      "halls free projective extension",
      "countable pappian projective planes",
      "main result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}