{"paper":{"title":"An AEC satisfying the disjoint amalgamation property, has arbitrarily large models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Adi Jarden","submitted_at":"2014-04-13T01:03:40Z","abstract_excerpt":"We study AECs without assuming the amalgamation property in general. We do assume the disjoint amalgamation property in a specific cardinality lambda and assume that there is no maximal model in \\lambda.\n  Under these hypotheses, we prove the following: 1. for every model, M, of cardinality \\lambda, and every \\mu>\\lambda, we can find a model M^* of cardinality \\mu, extending M. 2.(\\lambda,\\lambda,\\mu)-amalgalmation property: for every three models M,N,M^* of cardinalities \\lambda,\\lambda,\\mu, respectively, if M<M^* and M<N then we can amalgamate M^* and N over M."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3335","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"}