{
  "abstract": "Andrews, Ganchev, Kuyper, Lempp, Miller, A.\\ Soskova, and M.\\ Soskova conjectured that skip-cototality coincides with weak cototality. We show that the conjecture is false by constructing a $Π^0_2$ set whose skip does not have a cototal degree. We further adapt this construction to obtain additional results. We prove that for each odd $n$, there is a $Π^0_{n+1}$ degree whose $n$-iterated skip does not have a cototal degree. We show that there is a $Π^0_2$ degree which does not contain an introenumerable set.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14399",
  "author_total": 1,
  "authors": [
    {
      "name": "Taeyoung Em"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ff4vzy39geptt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14399",
  "fulltext_url": null,
  "id": "ff4vzy39geptt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14399",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.LO"
    ],
    [
      "openalex",
      "1703|Computability, Logic, AI Algorithms"
    ]
  ],
  "openalex": "W7221836265",
  "pdf_url": "https://arxiv.org/pdf/2610.14399",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ff4vzy39geptt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14399",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14399"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Controlling The Skips of Arithmetic Sets",
  "title_text": "Controlling The Skips of Arithmetic Sets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/ff4vzy39geptt",
  "venue": "arXiv",
  "versions": []
}