{
  "id": "1907.13360",
  "version": "v1",
  "published": "2019-07-31T08:26:39.000Z",
  "updated": "2019-07-31T08:26:39.000Z",
  "title": "Complexity in Young's Lattice",
  "authors": [
    "Alexander Wires"
  ],
  "comment": "13 pages",
  "categories": [
    "math.CO",
    "math.LO"
  ],
  "abstract": "We investigate the complexity of the partial order relation of Young's lattice. The definable relations are characterized by establishing the maximal definability property modulo the single automorphism given by conjugation; consequently, as an ordered set Young's lattice has an undecidable elementary theory and is inherently non-finitely axiomatizable but every ideal generates a finitely axiomatizable universal class of equivalence relations. We end with conjectures concerning the complexities of the $\\Sigma_1$ and $\\Sigma_2$-theories.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-31T08:26:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A17",
      "05A18"
    ],
    "keywords": [
      "complexity",
      "maximal definability property modulo",
      "partial order relation",
      "ordered set youngs lattice",
      "equivalence relations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}