%0 Journal Article
%T Abstract decomposition theorem and applications
%A Rami Grossberg
%A Olivier Lessmann
%J Mathematics
%D 2005
%I arXiv
%X Let K be an Abstract Elementary Class. Under the asusmptions that K has a nicely behaved forking-like notion, regular types and existence of some prime models we establish a decomposition theorem for such classes. The decomposition implies a main gap result for the class K. The setting is general enough to cover \aleph_0-stable first-order theories (proved by Shelah in 1982), Excellent Classes of atomic models of a first order tehory (proved Grossberg and Hart 1987) and the class of submodels of a large sequentially homogenuus \aleph_0-stable model (which is new).
%U http://arxiv.org/abs/math/0509707v1