{"paper":{"title":"Transferring Symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Monica VanDieren","submitted_at":"2015-07-07T23:52:00Z","abstract_excerpt":"In this paper, we apply results of \\cite{Va3} and use towers to transfer symmetry from $\\mu^+$ down to $\\mu$ in superstable abstract elementary classes without using extra set-theoretic assumptions or tameness.\n  Theorem. Suppose $\\mathcal{K}$ is an abstract elementary class satisfying the amalgamation and joint embedding properties and that $\\mathcal{K}$ is both $\\mu$- and $\\mu^+$-superstable. If $\\mathcal{K}$ has symmetry for non-$\\mu^+$-splitting, then $\\mathcal{K}$ has symmetry for non-$\\mu$-splitting.\n  This is a new application of towers which were introduced by Shelah and Villaveces \\ci"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01991","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"}