{
  "abstract": "We examine various applications of logic to $\\mathrm{AW}^*$-algebras, particularly the monotone completeness conjecture. We develop a model theory for $\\mathrm{AW}^*$-algebras equipped with a faithful normalized quasitrace. Using this language, we provide a separable coding which allows us to reduce the finite case of the monotone completeness conjecture to monotone sequential completeness of $\\mathrm{II}_1$ $\\mathrm{AW}^*$-factors. Combining an explicit recursive axiomatization with the completeness theorem for continuous logic, we show that this case of the conjecture, and Kaplansky's problem whether every $\\mathrm{AW}^*$-factor of type $\\mathrm{II}_1$ is a von Neumann algebra, are each equivalent in ZFC to a $Π^0_2$ sentence of arithmetic, so that their answers are the same in every $ω$-model of ZFC. We also consider real $\\mathrm{AW}^*$-algebras. Here the Baer-$*$-ring notion of an abelian projection must be distinguished from commutativity; following the real-operator-algebra terminology we call the former semi-abelian. Handelman's matrix theorem implies that a real $\\mathrm{AW}^*$-algebra with no nonzero central semi-abelian projection has $\\mathrm{AW}^*$ complexification. We answer a number of other open problems in real $\\mathrm{AW}^*$-algebras.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17435",
  "author_total": 1,
  "authors": [
    {
      "name": "Jananan Arulseelan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5ezmgfvhxemct.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17435",
  "fulltext_url": null,
  "id": "5ezmgfvhxemct",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17435",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.LO"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7221821301",
  "pdf_url": "https://arxiv.org/pdf/2610.17435",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5ezmgfvhxemct.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.17435",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17435"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Model theory of quasitracial $\\mathrm{AW}^*$-algebras and the absoluteness of monotone completeness",
  "title_text": "Model theory of quasitracial AW^*-algebras and the absoluteness of monotone completeness",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/5ezmgfvhxemct",
  "venue": "arXiv",
  "versions": []
}