Gabe Conant : Independence in Strongly Minimal Theories

Posted by Gabriel Conant , part of the Louise Hay Logic Seminar.

At

May 2, 2013, 3 p.m.

In

SEO 427

Abstract

We will define and discuss five notions of independence, which are frequently studied in an arbitrary first order theory. After assuming the theory in question has the property that algebraic closure satisfies exchange, we will add a sixth notion of dimensional independence, and see how it fits in with the others. Finally, we prove the equivalence of all six notions in strongly minimal theories with infinite algebraic closure. Altogether, this gives a characterization of independence that avoids any explicit mention of Morley rank or stability, but still demonstrates much of the same good behavior.