Model theory of difference fields-Reference-Cited by-同舟云学术

Model theory of difference fields

Published:1999-04-08 Issue:8 Volume:351 Page:2997-3071
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Chatzidakis Zoé,Hrushovski Ehud

Abstract

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 .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1999-351-08/S0002-9947-99-02498-8/S0002-9947-99-02498-8.pdf

Reference35 articles.

1. The elementary theory of finite fields;Ax, James;Ann. of Math. (2),1968

2. Locally modular theories of finite rank;Buechler, Steven;Ann. Pure Appl. Logic,1986

3. Definable sets over finite fields;Chatzidakis, Zoé;J. Reine Angew. Math.,1992

4. G. Cherlin, E. Hrushovski, Large finite structures with few 4-types, preprint 1998 (earlier version: Smoothly approximable structures, 1994).

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