{
  "abstract": "Every computable preorder relation on the natural numbers is the order of consistency strength for the membership assertions \"$n\\in A$\" in some computably enumerable set $A$. Moreover, for every computably enumerable list of theories $T_0,T_1,T_2,\\ldots$, each extending PA, there is a computably enumerable set $A$ such that each $T_n$ is equiconsistent over PA with the membership assertion $n\\in A$. And similarly for both results when using instead the nonmembership assertions $n\\notin A$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24919",
  "author_total": 2,
  "authors": [
    {
      "name": "Joel David Hamkins"
    },
    {
      "name": "Atticus Stonestrom"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8641bbs5j75dc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24919",
  "fulltext_url": null,
  "id": "8641bbs5j75dc",
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  "landing_url": "https://arxiv.org/abs/2610.24919",
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  "licence_label": "arXiv licence",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.LO"
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      "openalex",
      "1703|Computability, Logic, AI Algorithms"
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  "openalex": "W7223057813",
  "pdf_url": "https://arxiv.org/pdf/2610.24919",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8641bbs5j75dc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24919",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24919"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "The pattern of consistency strength for membership in a computably enumerable set",
  "title_text": "The pattern of consistency strength for membership in a computably enumerable set",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/8641bbs5j75dc",
  "venue": "arXiv",
  "versions": []
}