{
  "abstract": "We study the Gödel--Löb provability logic $\\mathbf{GL}$ for finite derived topologies on the ordinals. Assuming GCH and the existence of a measurable cardinal $κ$ which carries a coherent sequence of normal measures $\\vec{U}$ with $o^{\\vec{U}}(κ)\\geqκ$, we obtain a cofinality and GCH preserving generic extension in which $\\text{Log}_d(κ,τ_n)=\\mathbf{GL}$ for every $n<ω$, where $τ_n$ is the $n$-th derived topology. The result answers a well-know open question. Extending Beklemishev's theorem, we show that in the same model, for every $k<ω$, $ \\text{Log}_d(κ;τ_{2k},τ_{2k+1})=\\mathbf{GLP}_2, $ where the two modalities of $\\mathbf{GLP}_2$ are interpreted respectively by $d_{2k}$ and $d_{2k+1}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29708",
  "author_total": 1,
  "authors": [
    {
      "name": "Mohammad Golshani"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0eqywfpdgbajs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29708",
  "fulltext_url": null,
  "id": "0eqywfpdgbajs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29708",
  "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"
    ],
    [
      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7214366755",
  "pdf_url": "https://arxiv.org/pdf/2609.29708",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0eqywfpdgbajs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29708",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29708"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Completeness of the Gödel--Löb Provability Logic for Finite Derived Ordinal Topologies",
  "title_text": "Completeness of the Gödel--Löb Provability Logic for Finite Derived Ordinal Topologies",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/0eqywfpdgbajs",
  "venue": "arXiv",
  "versions": []
}