Abstract decomposition theorem and applications
Rami Grossberg, Olivier Lessmann
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 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 0-stable model (which is new).
Create a lesson
Related papers
Pseudofinite abelian groups and asymptotic classes of finite abelian groups
Carlos Cordoba-Caycedo, Dario Garcia
Spectral Theory and Descriptive Combinatorics for Non-Regular Borel pmp Graphs
Cecelia Higgins, Pieter Spaas, Sofia Torelli
The strength of the minimum principle in constructive reverse mathematics
Tatsuji Kawai
Independence of premise for intuitionistic Zermelo-Fraenkel set theory
Patrick Uftring
Condensed Whitehead Problem
Spencer Unger, Jerry Wei
Points and their multiples on curves in powers of simple abelian varieties
David J. Smith