Uniqueness of Limit Models in Classes with Amalgamation

We prove: Main Theorem: Let \mathcal{K} be an abstract elementary class satisfying the joint embedding and the amalgamation properties with no maximal models of cardinality \mu. Let \mu be a cardinal above the the L\"owenheim-Skolem number of the class. If \mathcal{K} is \mu-Galois-stable, has no \mu-Vaughtian Pairs, does not have... Show more