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Preprint Number 1164

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1164. Amador Martin-Pizarro and Martin Ziegler
Equational theories of fields

Submission date: 19 February 2017


[Research partially supported by the program MTM2014-59178-P. Additionally, the first author conducted research with support of the program ANR-13-BS01-0006 Valcomo.]

A complete 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. In this short note, we prove that theory of proper extension of algebraically closed fields of some fixed characteristic is equational.

Mathematics Subject Classification: 03C45, 12H05

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Full text arXiv 1702.05735: pdf, ps.

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