{
  "abstract": "In this paper, we consider conservation results for iterated $β_n$-model reflection principles. Using these principles, we characterize the $Π^1_{m+2}$-, $Σ^1_{m+2}$- and $\\mathsf{B}(Π^1_{m+2})$-consequences of $Σ^1_{n+1}$-$\\mathsf{DC}_0$ and $Σ^1_{n+1}$-$\\mathsf{TDC}_0$ for $m \\leq n$. Here, $\\mathsf{B}(Π^1_{m+2})$ denotes the set of Boolean combinations of $Π^1_{m+2}$-formulas, and $\\mathsf{TDC}$ stands for transfinite $\\mathsf{DC}$. We also show that, in each case, the stronger theory has a super-exponential speed-up over the corresponding conservative subtheory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36982",
  "author_total": 1,
  "authors": [
    {
      "name": "Yudai Suzuki"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bjvxwb1kpazww.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36982",
  "fulltext_url": null,
  "id": "bjvxwb1kpazww",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36982",
  "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",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7224121748",
  "pdf_url": "https://arxiv.org/pdf/2610.36982",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bjvxwb1kpazww.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.36982",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36982"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Dependent choice and iterated beta_n-model reflection",
  "title_text": "Dependent choice and iterated beta_n-model reflection",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/bjvxwb1kpazww",
  "venue": "arXiv",
  "versions": []
}