{
  "abstract": "When can a learner make only finitely many prediction errors along every infinite sequence labeled by a fixed, unknown hypothesis? We characterize this form of consistency for arbitrary binary hypothesis classes in ZFC, without requiring a uniform mistake bound. The characterization uses a single linear order on finite realizable traces. Each trace selects its least subtrace, and the order must satisfy two conditions: conflicting traces select different subtraces, and the order is well-founded on the traces of each fixed target. These conditions induce a learner whose selected evidence decreases on every mistake. Conversely, a consistent learner yields such an order through canonical mistake transcripts and the Kleene--Brouwer ordering. The result provides a representation of consistent prediction by finite evidence, answering a question of Lu (2024).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28551",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhou Lu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b0jb9dcdt2c64.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28551",
  "fulltext_url": null,
  "id": "b0jb9dcdt2c64",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28551",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1703|Computability, Logic, AI Algorithms"
    ]
  ],
  "openalex": "W7214337218",
  "pdf_url": "https://arxiv.org/pdf/2609.28551",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b0jb9dcdt2c64.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:21Z",
      "native_id": "2609.28551",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28551"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "An Order-Theoretic Characterization of Consistent Inductive Inference",
  "title_text": "An Order-Theoretic Characterization of Consistent Inductive Inference",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:21Z",
  "url": "https://research.draconitic.com/paper/b0jb9dcdt2c64",
  "venue": "arXiv",
  "versions": []
}