Model Theory of Differentially Closed Fields with a Generic Automorphism

Abstract

E. Hrushovski proved tha the theory of difference-differential fields has a model companion. We prove this result and other maind properties of this theory that we call DCFA. We describe the SU rank a its relation with transcendence degree. We prove a version of Zilber's dichotomy and we give a description of Abelian definable groups.