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 solveâ€¦ (More)

We prove a categoricity transfer theorem for tame abstract elementary classes. Theorem 0.1. Suppose that K is a Ï‡-tame abstract elementary class and satisfies the amalgamation and joint embeddingâ€¦ (More)

Grossberg and VanDieren have started a program to develop a stability theory for tame classes (see [GrVa1]). We name some variants of tameness (Definitions 1.4 and 1.7) and prove the following.â€¦ (More)

We prove: Theorem 0.1 (Main Theorem). Let K be an AEC and Î¼ > LS(K). Suppose K satisfies the disjoint amalgamation property for models of cardinality Î¼. If K is Î¼-Galois-stable, does not have longâ€¦ (More)