Categoricity in abstract elementary classes with no maximal models

CITY IN ABSTRACT ELEMENTARY CLASSES WITH NO MAXIMAL MODELS MONICA VANDIEREN Abstract. The results in this paper are in a context of abstract elementary classes identified by Shelah and Villaveces in which the amalgamation property is not assumed. The long-term goal is to solve Shelah's Categoricity Conjecture in this context. Here we tackle a problem of Shelah and Villaveces by proving that in their context, the uniqueness of limit models follows from categoricity under the assumption that the subclass of amalgamation bases is closed under unions of bounded, Kincreasing chains.

• Type: Journal
• Year: 2006
• Where: APAL
• Authors: Monica Van Dieren
• Keywords: Abstract Elementary Classes, Amalgamation Property, APAL 2006, MAXIMAL MODELS MONICA