Stability, Categoricity and Axiomatization of Abstract Elementary Classes

We extend current results on abstract elementary classes (AECs) in terms of stability, categoricity and axiomatization theorems. In most cases, we assume the existence of a monster model as well as tameness. The first two chapters introduce readers to the major questions and basic notions of AECs. The subsequent four chapters are the author’s papers written during his PhD program, each with its own abstract, introduction and results. The last chapter uses known results to derive a new categoricity transfer.