An invariant for difference field extensions

Abstract

In this paper we introduce a new invariant (the distant degree) for difference field extensions of finite transcendence degree, and we explore some of its properties. We also discuss a generalisation of this invariant and of the limit degree to groups with an automorphism.

After posting the previous version, we discovered the work of Willis on totally disconnected locally compact groups. Over a large area of overlap, our "distant degree" invariant of an automorphism agrees with Willis' {\em scale}. In the new version we describe the relations between the two frameworks. 14pp. July 2011: Small changes