{
  "abstract": "The Arthur-Nimue-Merlin degrees are a generalization of the Turing degrees introduced by Kihara as a tangible description of the partially ordered set of Lawvere-Tierney topologies on the effective topos (equivalently, subtoposes of the effective topos). They are defined in terms of a three-player game that introduces both angelic and demonic non-determinism into oracle queries. We construct an order embedding of the Turing degrees with their order reversed into the Arthur-Nimue-Merlin degrees, whose image we call the \"co-Turing degrees\"; we then study the order relationship of these co-Turing degrees with the (naturally embedded) Turing degrees within the Arthur-Nimue-Merlin degrees. This is a short version of arXiv:2603.19946, focused on the main results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08319",
  "author_total": 2,
  "authors": [
    {
      "name": "Jean Abou Samra"
    },
    {
      "name": "David A. Madore"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c23jyh6qvh947.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08319",
  "fulltext_url": null,
  "id": "c23jyh6qvh947",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08319",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LO"
    ],
    [
      "arxiv",
      "math.LO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08319",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c23jyh6qvh947.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.08319",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08319"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "An order-reversing embedding of Turing degrees into Arthur-Nimue-Merlin degrees (short version)",
  "title_text": "An order-reversing embedding of Turing degrees into Arthur-Nimue-Merlin degrees (short version)",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:49Z",
  "url": "https://research.draconitic.com/paper/c23jyh6qvh947",
  "venue": "arXiv",
  "versions": []
}