Abstract decomposition theorem and applications

Details Abstract decomposition theorem and applications Abstract decomposition theorem and applications

2005-09-29

arxiv.org/abs/math/0509707v1

Contemporary Mathematics, Vol 380, (2005), pp. 73--108

Mathematics

Logic

36 pages

Scientific paper

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).

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