Model theory of difference fields

Authors
Chatzidakis, Z Hrushovski, E
Citation
Z. Chatzidakis et E. Hrushovski, Model theory of difference fields, T AM MATH S, 351(8), 1999, pp. 2997-3071
Citations number
36
Categorie Soggetti
Mathematics
Journal title
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
00029947 → ACNP
Volume
351
Issue
8
Year of publication
1999
Pages
2997 - 3071
Database
ISI
SICI code
0002-9947(199908)351:8<2997:MTODF>2.0.ZU;2-5
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 differenc e equations. We show that an arbitrary formula may be reduced into one-dime nsional ones, and analyze the possible internal structures on the one-dimen sional formulas when the characteristic is 0.