{
  "id": "1610.00878",
  "version": "v1",
  "published": "2016-10-04T07:33:31.000Z",
  "updated": "2016-10-04T07:33:31.000Z",
  "title": "Reverse mathematics of the finite downwards closed subsets of $\\mathbb{N}^k$ ordered by inclusion",
  "authors": [
    "Florian Pelupessy"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We show that the well-partial orderedness of the finite downwards closed subsets of $\\mathbb{N}^k$ ,ordered by inclusion, is equivalent to the well-foundedness of the ordinal $\\omega^{\\omega^\\omega}$. This was conjectured to be so by Hatzikiriakou and Simpson.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-04T07:33:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03B30",
      "03F15",
      "06A06"
    ],
    "keywords": [
      "finite downwards closed subsets",
      "reverse mathematics",
      "well-partial orderedness",
      "equivalent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}