Submission date: 28 July 2009.

Abstract:

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

Mathematics Subject Classification: 12L12, 13L05, 03C60

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