{
  "id": "2401.11807",
  "version": "v1",
  "published": "2024-01-22T10:11:10.000Z",
  "updated": "2024-01-22T10:11:10.000Z",
  "title": "The weakness of finding descending sequences in ill-founded linear orders",
  "authors": [
    "Jun Le Goh",
    "Arno Pauly",
    "Manlio Valenti"
  ],
  "comment": "4 pages",
  "categories": [
    "math.LO",
    "cs.LO",
    "math.CO"
  ],
  "abstract": "We prove that the Weihrauch degree of the problem of finding a bad sequence in a non-well quasi order ($\\mathsf{BS}$) is strictly above that of finding a descending sequence in an ill-founded linear order ($\\mathsf{DS}$). This corrects our mistaken claim in arXiv:2010.03840, which stated that they are Weihrauch equivalent. We prove that K\\\"onig's lemma $\\mathsf{KL}$ is not Weihrauch reducible to $\\mathsf{DS}$ either, resolving the main open question raised in arXiv:2010.03840.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-22T10:11:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03D30",
      "03D78",
      "06A75"
    ],
    "keywords": [
      "ill-founded linear order",
      "finding descending sequences",
      "non-well quasi order",
      "main open question",
      "mistaken claim"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}