TY - JOUR
T1 - Toward categoricity for classes with no maximal models
AU - Shelah, Saharon
AU - Villaveces, Andrés
PY - 1999/3/21
Y1 - 1999/3/21
N2 - We provide here the first steps toward a Classification Theory of Abstract Elementary Classes with no maximal models, plus some mild set theoretical assumptions, when the class is categorical in some λ greater than its Löwenheim-Skolem number. We study the degree to which amalgamation may be recovered, the behaviour of non μ-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 Łós Conjecture for these classes. Further results are in preparation.
AB - We provide here the first steps toward a Classification Theory of Abstract Elementary Classes with no maximal models, plus some mild set theoretical assumptions, when the class is categorical in some λ greater than its Löwenheim-Skolem number. We study the degree to which amalgamation may be recovered, the behaviour of non μ-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 Łós Conjecture for these classes. Further results are in preparation.
KW - Abstract elementary classes
KW - Categoricity
KW - Classification theory
KW - Stability
UR - http://www.scopus.com/inward/record.url?scp=0033590737&partnerID=8YFLogxK
U2 - 10.1016/S0168-0072(98)00015-3
DO - 10.1016/S0168-0072(98)00015-3
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AN - SCOPUS:0033590737
SN - 0168-0072
VL - 97
SP - 1
EP - 25
JO - Annals of Pure and Applied Logic
JF - Annals of Pure and Applied Logic
IS - 1-3
ER -