Independence in tame abstract elementary classes

This is the title of a talk given at the 2015 JMM (Special session on beyond first order model theory) in San Antonio on Jan. 11, 2015. The talk presents a corresponding paper. Here are the slides.


Good frames are one of the main notions in Shelah's classification theory for abstract elementary classes. Roughly speaking, a good frame describes a local forking-like notion for the class. In Shelah's book, the theory of good frames is developped over hundreds of pages, and many results rely on GCH-like hypotheses and sophisticated combinatorial set theory. We argue that dealing with good frames is much easier if one makes the global assumption of tameness (a locality condition introduced by Grossberg and VanDieren). In particular, we prove ZFC results on the existence of good frames and other forking-like notions in AECs.