Monica VanDieren - Bogota Abstract

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

Title:  AECs with no maximal models.

Abstract:  One of the fundamental conjectures in the study of AECs is Shelah's Categoricity Conjecture. I will begin the talk by highlighting several partial results. Then, I will elaborate on the work of Shelah and Villaveces in categorical AECs with no maximal models under GCH. My main focus will be on their proofs of density of amalgamation bases and existence of limit models.

Limit models play an important role in several partial results towards Shelah's Categoricity Conjecture. The power of limit models comes from showing their uniqueness. Shelah and Villaveces provide many tools for showing the uniqueness of limit models, but ultimately they leave this problem open. In the afternoon discussion, I will explain my solution to the uniqueness of limit models.