{
  "abstract": "Gödel-Löb provability logic $\\GL$ is a propositional modal system that on one hand enjoys completeness with respect to conversely well-founded Kripke frames and on the other hand captures all modal principles about $\\PA$-provability that are provable in $\\PA$ itself. In the present paper we carry out an initial investigation into the question of what the infinitary counterpart of $\\GL$ is. We develop a non-well-founded deep inference proof system $\\dgla$ for the modal language with at most countably infinite conjunctions and disjunctions. We show that the calculus is sound and complete for well-founded transitive Kripke frames. Using Kripke-Platek set theory we develop an interpretation of the infinitary modal language in terms of infinitary provability over admissible sets. Then we show that a natural Hilber-style variant of infinitary $\\GL$ is sound for this interpretation. We leave open, however, the question if $\\dgla$ proves any additional theorems in comparison with the Hilbert-style calculus. Nevertheless, under certain conditions we do show that the infinitary provability logic arising from certain admissible sets lies between the set of theorems of the Hilbert-style calculus and the non-well-founded deep inference system.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24795",
  "author_total": 3,
  "authors": [
    {
      "name": "Mojtaba Mojtahedi"
    },
    {
      "name": "Fedor Pakhomov"
    },
    {
      "name": "Giovanni Soldà"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9pes2btq0ezhk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24795",
  "fulltext_url": null,
  "id": "9pes2btq0ezhk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24795",
  "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": "W7214014229",
  "pdf_url": "https://arxiv.org/pdf/2609.24795",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9pes2btq0ezhk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24795",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24795"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Infinitary provability logic",
  "title_text": "Infinitary provability logic",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/9pes2btq0ezhk",
  "venue": "arXiv",
  "versions": []
}