Equational theories of fields

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Journal of Symbolic Logic 85 (2):828-851 (2020)
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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.

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10.1017/jsl.2020.13

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Citations of this work

Semi-Equational Theories.Artem Chernikov & Alex Mennen - forthcoming - Journal of Symbolic Logic:1-32.

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References found in this work

Lovely pairs of models.Itay Ben-Yaacov, Anand Pillay & Evgueni Vassiliev - 2003 - Annals of Pure and Applied Logic 122 (1-3):235-261.
The indiscernible topology: A mock zariski topology.Markus Junker & Daniel Lascar - 2001 - Journal of Mathematical Logic 1 (01):99-124.
Imaginaries in pairs of algebraically closed fields.Anand Pillay - 2007 - Annals of Pure and Applied Logic 146 (1):13-20.

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