{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:TKT6LMKA4RSIBZRI7CIZCWZTFY","short_pith_number":"pith:TKT6LMKA","schema_version":"1.0","canonical_sha256":"9aa7e5b140e46480e628f891915b332e3e5d4faf57461a5d31b7aa3cf151945b","source":{"kind":"arxiv","id":"1404.3335","version":2},"attestation_state":"computed","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\\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