Submission date: 13 April 2014.

Abstract:

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. Under these hypotheses, we prove the following: 1. for every model, M, of cardinality λ, and every μ>λ, we can find a model M^* of cardinality μ, extending M. 2.(λ,λ,μ)-amalgalmation property: for every three models M,N,M^* of cardinalities λ,λ,μ, respectively, if M < M^* and M < N then we can amalgamate M^* and N over M.

Mathematics Subject Classification:

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Full text arXiv 1404.3335: pdf, ps.