{"paper":{"title":"Uniqueness of Limit Models in Classes with Amalgamation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Andres Villaveces, Monica VanDieren, Rami Grossberg","submitted_at":"2015-07-08T12:13:42Z","abstract_excerpt":"We prove:\n  Main Theorem: Let $\\mathcal{K}$ be an abstract elementary class satisfying the joint embedding and the amalgamation properties with no maximal models of cardinality $\\mu$. Let $\\mu$ be a cardinal above the the L\\\"owenheim-Skolem number of the class. If $\\mathcal{K}$ is $\\mu$-Galois-stable, has no $\\mu$-Vaughtian Pairs, does not have long splitting chains, and satisfies locality of splitting, then any two $(\\mu,\\sigma_\\ell)$-limits over $M$, for $\\ell\\in\\{1,2\\}$, are isomorphic over $M$.\n  This theorem extends results of Shelah from \\cite{Sh394}, \\cite{Sh576}, \\cite{Sh600}, Kolman a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02118","kind":"arxiv","version":2},"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"}