Model theory of difference fields

Chatzidakis, Zoé; Hrushovski, Ehud

doi:10.1090/S0002-9947-99-02498-8

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ISSN 1088-6850(online) ISSN 0002-9947(print)

Model theory of difference fields

Authors: Zoé Chatzidakis and Ehud Hrushovski
Journal: Trans. Amer. Math. Soc. 351 (1999), 2997-3071
MSC (1991): Primary 03C60; Secondary 03C45, 08A35, 12H10
Posted: April 8, 1999
MathSciNet review: 1652269
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Abstract: A difference field is a field with a distinguished automorphism $\sigma$ . 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 $0$ .

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