MONDAY, April 29, 2013

MODEL THEORY SEMINAR: 5:00 P.M., WeH 8220, Will Boney, Carnegie Mellon University

TITLE: Forking in Abstract Elementary Classes, Part 4.

ABSTRACT:

In this series, we detail joint work with Rami Grossberg to develop a forking-like relation over models, for Abstract Elementary Classes under mild assumptions (stability, tameness, type-shortness, and existence). This replaces and extends a much more complicated notion of Shelah called good frame. After covering the basic properties of this relation, we will explore extensions, such as the $U$ rank and local character. Parts of this theory are developed for a broader family of classes of structures than AECs (what is considered by Shelah the broadest framework allowing classification theory). This newer framework covers not only metric structures but even the logics $L_{\kappa, \lambda}$.