{"paper":{"title":"Density of uniqueness triples from the diamond axiom","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Adi Jarden, Ari Meir Brodsky","submitted_at":"2018-04-29T15:18:43Z","abstract_excerpt":"We work with a pre-$\\lambda$-frame, which is an abstract elementary class (AEC) endowed with a collection of basic types and a non-forking relation satisfying certain natural properties with respect to models of cardinality $\\lambda$.\n  We investigate the density of uniqueness triples in a given pre-$\\lambda$-frame $\\mathfrak s$, that is, under what circumstances every basic triple admits a non-forking extension that is a uniqueness triple. Prior results in this direction required strong hypotheses on $\\mathfrak s$.\n  Our main result is an improvement, in that we assume far fewer hypotheses on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10952","kind":"arxiv","version":3},"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"}