{
  "abstract": "We study the equational theory and subvarieties of the variety $\\mathcal V$ generated by $(\\mathbb N_0,\\min,+)$. We prove that a subvariety of $\\mathcal V$ is proper if and only if it is locally finite, equivalently, if and only if it satisfies a power-stabilization identity. Every finite member generates a hereditarily finitely based variety with a finite subvariety lattice. In contrast, the periodic subvarieties defined by $x^m=x^{m+1}$ are nonfinitely based for $m\\geq2$. We construct a strictly descending chain of nonfinitely based subvarieties and three varieties generated by explicit reduced products, each with a decidable equational theory. The smallest is a limit variety: it is nonfinitely based, and every proper subvariety has an absolute finite identity basis. The subvariety lattice of $\\mathcal V$ has cardinality continuum. In fact, the interval between the first reduced-product variety and the subvariety defined by $x^2=x^3$ already has this cardinality, and all its members are nonfinitely based. We also give a hereditarily finitely based example with an infinite subvariety lattice. The constructions use finite convex models and recognition quotients.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03715",
  "author_total": 2,
  "authors": [
    {
      "name": "Yilin Zhou"
    },
    {
      "name": "Zidong Gao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/28qdv4z4s9mst.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03715",
  "fulltext_url": null,
  "id": "28qdv4z4s9mst",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03715",
  "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",
      "math.LO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03715",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/28qdv4z4s9mst.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.03715",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03715"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Equational theories of min-plus semirings",
  "title_text": "Equational theories of min-plus semirings",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/28qdv4z4s9mst",
  "venue": "arXiv",
  "versions": []
}