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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
Published electronically: 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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Additional Information

Zoé Chatzidakis
Affiliation: Université Paris 7, Case 7012, 2, place Jussieu, 75251 Paris Cedex 05, France
Email: zoe@logique.jussieu.fr

Ehud Hrushovski
Affiliation: Institute of Mathematics, The Hebrew University, Givat Ram, Jerusalem 91904, Israel
Email: ehud@sunset.ma.huji.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02498-8
Keywords: Model theory applied to algebra, difference fields
Received by editor(s): August 14, 1996
Published electronically: April 8, 1999
Additional Notes: The second author was supported by NSF grants DMS 9106711 and 9400894
Article copyright: © Copyright 1999 American Mathematical Society