Submission date: 10 December 2014.

Abstract:

We introduce a new device in the study of abstract elementary classes: Galois Morleyization, which consists in expanding the models of the class with a relation for every Galois type of length less than a fixed cardinal κ. We show that an AEC is fully (<κ)-tame and type short if and only if Galois types are syntactic in the Galois Morleyization. We use this idea to make progress on the stability theory of tame and type short abstract elementary classes. We also prove strong structural results on good frames, an axiomatization of forking introduced by Shelah. Our main theorem is the construction of a global independence notion (with the properties of forking in a superstable first-order theory) from full tameness and shortness, amalgamation, and categoricity.

Mathematics Subject Classification: 03C48 (Primary) 03C45, 03C52, 03C55, 03C75, 03E55 (Secondary)

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Full text arXiv 1412.3313: pdf, ps.