Alice Medvedev : Model theory of difference fields: connections to algebraic geometry and rational dynamics

Posted by David E. Marker , part of the Logic Seminar.

At

Oct. 16, 2007, 4 p.m.

In

SEO 427

Abstract

A difference field is a field with a distinguished automorphism $\sigma$; for example, one can look at a field of characteristic $p$ and take $\sigma(x) = x^p$ to be the Frobenius automorphism. Model-theorists have things to say about the class of existentially-closed difference fields: it is first-order axiomatizable, and the resulting theory, called ACFA, is supersimple and generally nice. I will say things certain minimal definable sets in ACFA, namely about solution sets of $\sigma(x) = f(x)$ for rational functions $f$.