{
  "abstract": "We show that the satisfiability problem for Strategy Logic introduced by Mogavero, Murano, and Vardi is $Π^1_\\infty$-complete, and, more strongly, computably isomorphic to true second-order arithmetic. The lower bound is established for the next-time Boolean-goal fragment of Strategy Logic. Consequently, Strategy Logic is not recursively axiomatizable, even with effectively defined $ω$-rules.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16173",
  "author_total": 1,
  "authors": [
    {
      "name": "Tikhon Pshenitsyn"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7f7vqgdq1129s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16173",
  "fulltext_url": null,
  "id": "7f7vqgdq1129s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16173",
  "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",
      "1702|Logic, Reasoning, and Knowledge"
    ]
  ],
  "openalex": "W7213407443",
  "pdf_url": "https://arxiv.org/pdf/2609.16173",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7f7vqgdq1129s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.16173",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16173"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Exact Complexity of the Satisfiability Problem for Strategy Logic",
  "title_text": "Exact Complexity of the Satisfiability Problem for Strategy Logic",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/7f7vqgdq1129s",
  "venue": "arXiv",
  "versions": []
}