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Friday, November 11, 2005

**Abstract:** Generalized amalgamation properties were introduced by Shelah in the (non-first order) context of classes of atomic models and were also used in the proof of the Main Gap theorem. In my thesis, I studied generalized type-amalgamation in the context of simple theories, what is now called n-simplicity. Initially the similarity between the type amalgamation (the simple case) and model-amalgamation (atomic case) was largely superficial, however the recent developments brought the two approaches closer together. My talk will have two parts. In the first, I will present the definitions of generalized amalgamation properties in the context of abstract elementary classes, and talk about some of the results of the joint work with Rami Grossberg on this topic. The second part will be devoted to n-simplicity.