{
  "abstract": "Using set-theoretic methods, we prove that every $\\mathrm{AW}^*$-algebra is normal, resolving a question of Wright that has stood open for 46 years. This was previously known in the case of $\\mathrm{AW}^*$-factors, by work of Saitô and Wright. We also show that if there is a model $V$ of $\\mathrm{ZFC}$ with an $\\mathrm{AW}^*$-algebra that fails to be monotone complete, then in some forcing extension of $V$ there is an $\\mathrm{AW}^*$-factor that fails to be monotone complete, implying that any $\\mathrm{ZFC}$ proof that all $\\mathrm{AW}^*$-factors are monotone complete yields a $\\mathrm{ZFC}$ proof that all $\\mathrm{AW}^*$-algebras are monotone complete. Both results build on transfer principles for Boolean-valued factor representations originally developed by Ozawa. This work was assisted by the Danus LLM orchestration system.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10218",
  "author_total": 2,
  "authors": [
    {
      "name": "Jananan Arulseelan"
    },
    {
      "name": "James E. Hanson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/75gnzfsr4swvb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10218",
  "fulltext_url": null,
  "id": "75gnzfsr4swvb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10218",
  "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": "W7212145910",
  "pdf_url": "https://arxiv.org/pdf/2609.10218",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/75gnzfsr4swvb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.10218",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10218"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Every $\\mathrm{AW}^*$-Algebra is Normal",
  "title_text": "Every AW^*-Algebra is Normal",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/75gnzfsr4swvb",
  "venue": "arXiv",
  "versions": []
}