# Model theory of (partial) differential fields with an automorphism

#### Omar Leon Sanchez, University of Manchester. Part of the logic seminar series.

Given a model-complete theory T, we let T_s be the theory whose models are those of T equipped with an automorphism. In the case when T_s has a model companion, we say that TA exists. In this talk I will give a brief survey on results about the existence of TA and its properties. I will then try to explain why DCF_{0,m}A exists where DCF_{0,m} denotes the theory of differentially closed fields in characteristic zero with m commuting derivations.

Omar Leon Sanchez, University of Manchester