Monica VanDieren - New York Abstract

E-mail:  monica@math.stanford.edu
Homepage:  http://math.stanford.edu/~monica/home.html.

Title:  A Substitute for Saturation in AECs.

Abstract:  My work is in a context idenitified by Shelah and Villaveces in which the amalgamation property does not necessarily hold. The longterm goal is to solve Shelah's Categoricity Conjecture in this context. One of the first steps is to isolate a suitable notion of saturation. I have solved a conjecture of Shelah and Villaveces by proving the uniqueness of limit models, which will serve as our notion of saturation. In this talk I will highlight the history of Shelah's Categoricity Conjecture, describe the context of Shelah and Villaveces and explain how their conjecture can impact work towards the categoricity conjecture. I will end the talk with a description of a few of the features of my solution.