An invariant for difference field extensions (2009)
Chatzidakis, Zoé, Hrushovski, Ehud
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...
Universität Heidelberg IWR INF 368 (2008)
Zoé Chatzidakis, Charlotte Hardouin, Michael F. Singer
We compare several definitions of the Galois group of a linear difference equation that have arisen in algebra, analysis and model theory and show, that these groups are isomorphic over suitable...
Difference fields and descent in algebraic dynamics - I (2007)
Chatzidakis, Zoé, Hrushovski, Ehud
We draw a connection between the model-theoretic notions of modularity (or one-basedness), orthogonality and internality, as applied to difference fields, and questions of descent in in algebraic...
Difference fields and descent in algebraic dynamics, II (2007)
Chatzidakis, Zoé, Hrushovski, Ehud
This second part of the paper strengthens the descent theory described in the first part to rational maps, arbitrary base fields, and dynamics given by correspondences. We obtain in particular a...
On the Definitions of Difference Galois Groups (2007)
Chatzidakis, Zoé, Hardouin, Charlotte, Singer, Michael F.
We compare several definitions of the Galois group of a linear difference equation that have arisen in algebra, analysis and model theory and show, that these groups are isomorphic over suitable...
Model theory of difference fields (1999)
Zoé Chatzidakis, Ehud Hrushovski
Abstract. A difference field is a field with a distinguished automorphism σ. This paper studies the model theory of existentially closed difference fields. We introduce a dimension theory on...