Toward categoricity for classes with no maximal models
Abstract
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 LowenheimSkolem number. We study the degree to which amalgamation may be recovered, the behaviour of non musplitting 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 July 1997
 DOI:
 10.48550/arXiv.math/9707227
 arXiv:
 arXiv:math/9707227
 Bibcode:
 1997math......7227S
 Keywords:

 Mathematics  Logic