{
  "abstract": "For nearly sixty years, refinements of the Bell-Kochen-Specker theorem have concentrated on finite configurations, combinatorics and robustness; once a configuration is fixed, contextuality is witnessed by the inconsistency of a finite family of Boolean constraints. We study the theorem instead with infinitary real-valued logic and a model existence game. We axiomatize, in real-valued $L_{ω_1ω}$, the lattice of closed subspaces of a separable infinite-dimensional complex Hilbert space together with a quantum probability measure. In the standard models the theory recovers Gleason's theorem. Once the axiom that the measure is $\\{0,1\\}$-valued is adjoined, the theory has no models, standard or nonstandard, although every finite set of its axioms has one; a model existence game converts this infinitary inconsistency into finite inconsistent sets of interval commitments on the values of sentences. Over the standard models, the subsets of $[0,1]$ that formulas define through the values of the measure are exactly the $σ$-projective sets, the members of the least class containing the Borel sets and closed under complements, countable unions and projections along $\\mathbb{N}^\\mathbb{N}$; the classification is proved in ZFC. For a specified strategy in the game, the plays that complete the parity argument for the eighteen-ray configuration of Cabello, Estebaranz and García-Alcaine record the geometric identities between the occurrences of a ray in different contexts, and the use that the measure makes of them. Probabilities are tracked up to rational tolerances, and $σ$-additivity along a named basis selects the four-dimensional block in which the argument takes place. The refinement is thus not a smaller Kochen-Specker set but a finer analysis of the logical form of the obstruction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05656",
  "author_total": 2,
  "authors": [
    {
      "name": "Olivia Aubone"
    },
    {
      "name": "José Iovino"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dktms46ckqw05.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05656",
  "fulltext_url": null,
  "id": "dktms46ckqw05",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05656",
  "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",
      "math.LO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05656",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dktms46ckqw05.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.05656",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05656"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Infinitary real-valued logic and a refinement of the Kochen-Specker theorem",
  "title_text": "Infinitary real-valued logic and a refinement of the Kochen-Specker theorem",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:29Z",
  "url": "https://research.draconitic.com/paper/dktms46ckqw05",
  "venue": "arXiv",
  "versions": []
}