{"paper":{"title":"The Joint Embedding Property and Maximal Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Ioannis Souldatos, John T. Baldwin, Martin Koerwien","submitted_at":"2015-01-29T00:39:06Z","abstract_excerpt":"We introduce the notion of a `pure` Abstract Elementary Class to block trivial counterexamples. We study classes of models of bipartite graphs and show:\n  Main Theorem (cf. Theorem 3.5.2 and Corollary 3.5.6): If $(\\lambda_i : i \\le \\alpha<\\aleph_1)$ is a strictly increasing sequence of characterizable cardinals (Definition 2.1) whose models satisfy JEP$(<\\lambda_0)$, there is an $L_{\\omega_1,\\omega}$ -sentence $\\psi$ whose models form a pure AEC and\n  (1) The models of $\\psi$ satisfy JEP$(<\\lambda_0)$, while JEP fails for all larger cardinals and AP fails in all infinite cardinals.\n  (2) There"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07316","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"}