A survey on tame abstract elementary classes

Will Boney, Sebastien Vasey

Published 2015-11-30Version 1

We survey recent developments in the study of tame abstract elementary classes. We emphasize the role of abstract independence relations such as Shelah's good frames. As an application, we sketch a proof of a categoricity transfer in universal classes (due to the second author): $\mathbf{Theorem}$ If a universal class is categorical in cardinals of arbitrarily high cofinality, then it is categorical on a tail of cardinals.