{
  "abstract": "We introduce an ordinal-valued invariant of well-founded trees, called their type. We use type to give an alternative proof that the class of all well-founded trees is well-quasi-ordered by the homomorphism relation, and we establish a relationship between type and the usual ordinal rank of a well-founded tree, showing in particular that type provides a strictly coarser structural classification.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.02136",
  "author_total": 1,
  "authors": [
    {
      "name": "Jakub Smolík"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bgf4yj1fj6ww2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.02136",
  "fulltext_url": null,
  "id": "bgf4yj1fj6ww2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.02136",
  "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"
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      "openalex",
      "2608|Advanced Topology and Set Theory"
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  "openalex": "W7172387296",
  "pdf_url": "https://arxiv.org/pdf/2608.02136",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bgf4yj1fj6ww2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2608.02136",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.02136"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Types of well-founded trees and the homomorphism order",
  "title_text": "Types of well-founded trees and the homomorphism order",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/bgf4yj1fj6ww2",
  "venue": "arXiv",
  "versions": []
}