Model Theory of Valued Difference Fields

Abstract

In this thesis we investigate the model theoretic properties of valued difference fields, that is, valued fields equipped with a distinguished automorphism. We carry out this study in two different contexts depending on the interaction between the valuation and the distinguished automorphism. In both contexts we obtain analogues of the classical results from the model theory of valued fields. We also present a treatment of valued fields in equal characteristic p > 0 as valued difference fields equipped with the Frobenius endomorphism.