Toward Categoricity for Classes with no Maximal Models

by Shelah and Villaveces. [ShVi:635]
Annals Pure and Applied Logic, 1999
We provide here the first steps toward Classification Theory of Abstract Elementary Classes with no maximal models, plus some mild set theoretical assumptions, when the class is categorical in some lambda greater than its L{o}wenheim-Skolem number. We study the degree to which amalgamation may be recovered, the behaviour of non mu-splitting types. Most importantly, the existence of saturated models in a strong enough sense is proved, as a first step toward a complete solution to the Los Conjecture for these classes.

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