Forking and superstability in tame abstract elementary classes

This is the title of a talk given at the Classification Theory Workshop in NIMS (Daejeon, South Korea) on Aug. 9, 2014. The talk presents the corresponding paper. Here are the slides.


We prove that any tame abstract elementary class categorical in a suitable cardinal has a global good frame: a forking-like notion defined on all types of single elements. This gives the first known general construction of a good frame in ZFC. We show that we already obtain a well-behaved independence relation assuming only a superstability-like hypothesis instead of categoricity. These methods are applied to obtain an upward stability transfer theorem from categoricity and tameness, as well as new conditions for uniqueness of limit models.