Shelah-Villaveces revisited

We study uniqueness of limit models in abstract elementary classes (AECs) with no maximal models. We prove (assuming instances of diamonds) that categoricity in a cardinal of the form \mu^{+(n + 1)} implies the uniqueness of limit models of cardinality \mu^{+}, \mu^{++}, \ldots, \mu^{+n}. This sheds light on a paper... Show more