Abstract decomposition theorem and applications

2005/09/29 by Rami Grossberg, Olivier Lessmann
Mathematics · #math.LO #msc:03C45 #msc:03C52 #msc:03C05 #msc:03C95

paper · pdf

published as Contemporary Mathematics, Vol 380, (2005), pp. 73--108 · 36 pages

arxiv created 2005/09/29 · arxiv updated 2009/12/01

Abstract

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 ℵ₀-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 ℵ₀-stable model (which is new).

Related

• On Stability and Existence of Models in Abstract Elementary Classes
• Introduction to: classification theory for abstract elementary class
• Forking in Short and Tame Abstract Elementary Classes
• Constructing many atomic models in ℵ₁
• Limit Models in Strictly Stable Abstract Elementary Classes