{
  "id": "1408.0315",
  "version": "v2",
  "published": "2014-08-01T22:23:53.000Z",
  "updated": "2014-09-09T14:41:27.000Z",
  "title": "On better-quasi-ordering classes of partial orders",
  "authors": [
    "Gregory McKay"
  ],
  "comment": "v1: 45 pages, 8 figures; v2: 44 pages, 11 figures, minor corrections, fixed typos, new figures and some notational changes to improve clarity",
  "categories": [
    "math.LO"
  ],
  "abstract": "We provide a method of constructing better-quasi-orders by generalising a technique for constructing operator algebras that was developed by Pouzet. We then use this method to prove that certain transfinite classes of partial orders are better-quasi-ordered under embeddability. In particular, a class of countable partial orders is better-quasi-ordered whenever the class of indecomposable subsets of its members satisfies a natural strengthening of better-quasi-order. Our main result generalises theorems of Laver, Corominas and Thomass\\'e reguarding \\sigma-scattered linear orders and trees, countable forests and N-free partial orders respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-01T22:23:53.000Z",
      "abstract": "We provide a method for constructing better-quasi-orders by generalising a technique developed by Pouzet. We then use this method to prove that certain large classes of partial orders are better-quasi-ordered under embeddability. This result generalises theorems of Laver, Corominas and Thomass\\'e.",
      "comment": "45 pages, 8 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-09T14:41:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "06A07",
      "03E05",
      "06A06",
      "05C05"
    ],
    "keywords": [
      "partial orders",
      "better-quasi-ordering classes",
      "result generalises theorems",
      "large classes",
      "constructing better-quasi-orders"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}