{"paper":{"title":"Neostability in countable homogeneous metric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Gabriel Conant","submitted_at":"2015-04-09T19:11:13Z","abstract_excerpt":"Given a countable, totally ordered commutative monoid $\\mathcal{R}=(R,\\oplus,\\leq,0)$, with least element $0$, there is a countable, universal and ultrahomogeneous metric space $\\mathcal{U}_\\mathcal{R}$ with distances in $\\mathcal{R}$. We refer to this space as the $\\mathcal{R}$-Urysohn space, and consider the theory of $\\mathcal{U}_\\mathcal{R}$ in a binary relational language of distance inequalities. This setting encompasses many classical structures of varying model theoretic complexity, including the rational Urysohn space, the free $n^{\\text{th}}$ roots of the complete graph (e.g. the ran"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02427","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}