# Sh:635

• Shelah, S., & Villaveces, A. (1999). Toward categoricity for classes with no maximal models. Ann. Pure Appl. Logic, 97(1-3), 1–25.
• 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 Löwenheim-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.
• Current version: 1997-07-25_10 (37p) published version (25p)
Bib entry
@article{Sh:635,
author = {Shelah, Saharon and Villaveces, Andr{\'e}s},
title = {{Toward categoricity for classes with no maximal models}},
journal = {Ann. Pure Appl. Logic},
fjournal = {Annals of Pure and Applied Logic},
volume = {97},
number = {1-3},
year = {1999},
pages = {1--25},
issn = {0168-0072},
mrnumber = {1682066},
mrclass = {03C45 (03C35 03C52)},
doi = {10.1016/S0168-0072(98)00015-3},
note = {\href{https://arxiv.org/abs/math/9707227}{arXiv: math/9707227}},
arxiv_number = {math/9707227}
}