Model theory of difference fields
Zoé Chatzidakis, Ehud Hrushovski · Transactions of the American Mathematical Society · 1999
A difference field is a field with a distinguished automorphism σ \sigma . This paper studies the model theory of existentially closed difference fields. We introduce a dimension theory on formulas, and in particular on difference equations. We show that an arbitrary formula may be reduced into one-dimensional ones, and analyze the possible internal structures on the one-dimensional formulas when the characteristic is 0 0 .