{
  "abstract": "We give a column-avoidance modification of the no-least-join construction of Downey, Greenberg, Lewis, and Montalbán. We show that if $C$ is computably enumerable, $A,B<_T C$, and $A\\not\\leq_T B$, then for every noncomputable set $E$ there is a set $X\\leq_T C$ such that $B\\leq_T A\\oplus X$ and $E\\not\\leq_T X$. Consequently, for the corresponding Turing degrees $a,b,c$, the degrees $x\\leq c$ satisfying $b\\leq a\\vee x$ have no nonzero common lower bound; equivalently, no nonzero Turing cone contains all of them. This gives a negative answer to their Question 1.19.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02027",
  "author_total": 1,
  "authors": [
    {
      "name": "Patrizio Cintioli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1rg1sc8w1afkc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02027",
  "fulltext_url": null,
  "id": "1rg1sc8w1afkc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02027",
  "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",
      "1703|Computability, Logic, AI Algorithms"
    ]
  ],
  "openalex": "W7216152941",
  "pdf_url": "https://arxiv.org/pdf/2610.02027",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1rg1sc8w1afkc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.02027",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02027"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Cone Avoidance and the No-Least-Join Theorem",
  "title_text": "Cone Avoidance and the No-Least-Join Theorem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/1rg1sc8w1afkc",
  "venue": "arXiv",
  "versions": []
}