{"paper":{"title":"Categoricity and infinitary logics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Sebastien Vasey, Will Boney","submitted_at":"2015-08-13T19:22:02Z","abstract_excerpt":"We point out a gap in Shelah's proof of the following result:\n  $\\mathbf{Claim}$\n  Let $K$ be an abstract elementary class categorical in unboundedly many cardinals. Then there exists a cardinal $\\lambda$ such that whenever $M, N \\in K$ have size at least $\\lambda$, $M \\le N$ if and only if $M \\preceq_{L_{\\infty, \\text{LS} (K)^+}} N$.\n  The importance of the claim lies in the following theorem, implicit in Shelah's work:\n  $\\mathbf{Theorem}$\n  Assume the claim. Let $K$ be an abstract elementary class categorical in unboundedly many cardinals. Then the class of $\\lambda$ such that:\n  1) $K$ is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03316","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"}