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EQUATIONAL THEORIES OF FIELDS

Part of: Differential and difference algebra Model theory

Published online by Cambridge University Press:  15 July 2020

AMADOR MARTIN-PIZARRO  and
MARTIN ZIEGLER
AMADOR MARTIN-PIZARRO
Affiliation:
MATHEMATISCHES INSTITUT ALBERT-LUDWIGS-UNIVERSITÄT FREIBURGD-79104FREIBURG, GERMANYE-mail: pizarro@math.uni-freiburg.deE-mail: ziegler@uni-freiburg.de
MARTIN ZIEGLER
Affiliation:
MATHEMATISCHES INSTITUT ALBERT-LUDWIGS-UNIVERSITÄT FREIBURGD-79104FREIBURG, GERMANYE-mail: pizarro@math.uni-freiburg.deE-mail: ziegler@uni-freiburg.de
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Abstract

A first-order theory is equational if every definable set is a Boolean combination of instances of equations, that is, of formulae such that the family of finite intersections of instances has the descending chain condition. Equationality is a strengthening of stability. We show the equationality of the theory of proper extensions of algebraically closed fields and of the theory of separably closed fields of arbitrary imperfection degree.

Keywords

model theoryseparably closed fieldsdifferentially closed fieldsequationality

MSC classification

Primary: 03C45: Classification theory, stability and related concepts
Secondary: 12H05: Differential algebra
Type
Articles
Information
The Journal of Symbolic Logic , Volume 85 , Issue 2 , June 2020 , pp. 828 - 851
Copyright
© The Association for Symbolic Logic 2020

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