{"paper":{"title":"A Characterization of Uniqueness of Limit Models in Categorical Abstract Elementary Classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Monica M. VanDieren","submitted_at":"2015-11-29T23:36:06Z","abstract_excerpt":"In this paper we examine the task set forth by Shelah and Villaveces in \\cite{ShVi} of proving the uniqueness of limit models of cardinality $\\mu$ in $\\lambda$-categorical abstract elementary classes with no maximal models, where $\\lambda$ is some cardinal larger than $\\mu$. In \\cite{Va} and \\cite{Va-errata} we identified several gaps in the approach outlined in \\cite{ShVi}, and we added the assumption that the union of an increasing chain of limit models is a limit model.\n  Here we replace this assumption with the seemingly weaker statement that the union of an increasing and continuous chain"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.09112","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"}