{
  "abstract": "We show that for any henselian valued field of mixed characteristic $(0,p)$, the (existential) $\\mathcal{L}_{\\mathrm{val}}$-theory of the valued field is determined by the (existential) theory of the value group in $\\mathcal{L}_{\\mathrm{oag}}$ with a constant for $v(p)$ and the (existential) theory of the residue ring $\\mathcal{O}_v/(p)$ in an expansion $\\mathcal{L}_{\\mathrm{Witt}}$ of the language of rings, provided $\\mathcal{O}_v/(p)$ is semi perfect. We moreover show that the $\\mathcal{L}_{\\mathrm{Witt}}$-structure on $\\mathcal{O}_v/(p)$ is $\\mathcal{L}_{\\mathrm{ring}}$-definable using constants, and that this is exactly the structure induced on $\\mathcal{O}_v/(p)$ by the ambient valued field. As a consequence, we obtain a relative quantifier elimination result (eliminating $K$-quantifiers) in a suitable language for the theory of roughly deeply ramified henselian valued fields of mixed characteristic $(0,p)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15376",
  "author_total": 3,
  "authors": [
    {
      "name": "Franziska Jahnke"
    },
    {
      "name": "Margarete Ketelsen"
    },
    {
      "name": "Floris Vermeulen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d0xj25dvf02sj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15376",
  "fulltext_url": null,
  "id": "d0xj25dvf02sj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15376",
  "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.AC"
    ],
    [
      "arxiv",
      "math.LO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7213323007",
  "pdf_url": "https://arxiv.org/pdf/2609.15376",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d0xj25dvf02sj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15376",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15376"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "AKE principles in roughly deeply ramified henselian valued fields",
  "title_text": "AKE principles in roughly deeply ramified henselian valued fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/d0xj25dvf02sj",
  "venue": "arXiv",
  "versions": []
}