{"paper":{"title":"Superstability in Tame Abstract Elementary Classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Monica VanDieren","submitted_at":"2015-02-13T22:36:21Z","abstract_excerpt":"In this paper we address a problem posed by Shelah in 1999 to find a suitable notion for superstability for abstract elementary classes in which limit models of cardinality $\\mu$ are saturated.\n  Theorem 1. Suppose that $\\mathcal{K}$ is a $\\chi$-tame abstract elementary class with no maximal models satisfying the joint embedding property and the amalgamation property. Suppose $\\mu$ is a cardinal with $\\mu\\geq\\beth_{(2^{LS(\\mathcal{K})+\\chi})^+}$. Let $M$ be a model of cardinality $\\mu$. If $\\mathcal{K}$ is both $\\chi$-stable and $\\mu$-stable and satisfies the $\\mu$-superstability assumptions, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04144","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"}