{
  "abstract": "We compare two Polish presentations of separable real Banach lattices: closed sublattices of a universal lattice and closed ideals of $\\operatorname{FBL}[\\ell_1]$. We construct translations preserving lattice isometry in both directions, continuous and injective from sublattices to ideals and Borel in the reverse direction. Natural generation and Fremlin tensor operations are $\\boldsymbolΣ^0_2$-measurable with $G_δ$ graphs. Isometric lattice isomorphism in either universal coding is Borel bireducible with a complete orbit equivalence relation of Polish-group actions. Uniform monotonicity and order uniform smoothness are $\\boldsymbolΠ^0_3$-complete in both codings, whereas strict monotonicity, order smoothness, and order continuity are coanalytic. Abstract $L_p$ and AM-spaces form closed classes of sublattice codes. We also give explicit Borel bounds for atom counts, compact order intervals, and the lattice-isometry classes of $L_p[0,1]$, $\\ell_p$, and $c_0$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.08064",
  "author_total": 1,
  "authors": [
    {
      "name": "Mariusz Niwiński"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9n3dhhe7sep4g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.08064",
  "fulltext_url": null,
  "id": "9n3dhhe7sep4g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.08064",
  "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.FA"
    ],
    [
      "arxiv",
      "math.GN"
    ],
    [
      "arxiv",
      "math.LO"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7167926031",
  "pdf_url": "https://arxiv.org/pdf/2607.08064",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9n3dhhe7sep4g.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:09Z",
      "native_id": "2607.08064",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.08064"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Polish spaces of separable Banach lattices",
  "title_text": "Polish spaces of separable Banach lattices",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/9n3dhhe7sep4g",
  "venue": "arXiv",
  "versions": []
}