{
  "abstract": "We formulate a proof of Part~I of Martin's conjecture for order-preserving maps directly on the quotient of the reals by Turing equivalence. The assumptions are countable choice for reals, the perfect-set property for sets of reals, and continuous uniformization on a comeager domain. The argument applies under $\\mathsf{AD}+\\mathsf{DC}_{\\R}$ and inside the choiceless Solovay model. We then determine the exact consistency strength of the unrestricted order-preserving dichotomy as an axiom over $\\mathsf{ZF}+\\mathsf{AC}_ω(\\R)$: it is equiconsistent with $\\mathsf{ZFC}$ plus a strongly inaccessible cardinal.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14548",
  "author_total": 1,
  "authors": [
    {
      "name": "Liang Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8bkycnwe4vh07.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14548",
  "fulltext_url": null,
  "id": "8bkycnwe4vh07",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14548",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.LO"
    ],
    [
      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7221789383",
  "pdf_url": "https://arxiv.org/pdf/2610.14548",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8bkycnwe4vh07.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14548",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14548"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Order-preserving maps of the Turing degrees: regularity and consistency strength",
  "title_text": "Order-preserving maps of the Turing degrees: regularity and consistency strength",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/8bkycnwe4vh07",
  "venue": "arXiv",
  "versions": []
}