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Blossier, Thomas; Martin-Pizarro, Amador

A simple criterion. (Un critère simple.) (French. English summary) Zbl 1472.03034

Notre Dame J. Formal Logic 60, No. 4, 639-663 (2019).
Summary: In this article, we mimic the proof of the simplicity of the theory ACFA of generic difference fields in order to provide a criterion, valid for certain theories of pure fields and fields equipped with operators, which shows that a complete theory is simple whenever its definable and algebraic closures are controlled by an underlying stable theory.

Cited in 2 Documents

MSC:

03C60 Model-theoretic algebra
03C45 Classification theory, stability, and related concepts in model theory
12H05 Differential algebra
12H10 Difference algebra

Keywords:

simple theories; fields with operators; pseudo-algebraically closed fields
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\textit{T. Blossier} and \textit{A. Martin-Pizarro}, Notre Dame J. Formal Logic 60, No. 4, 639--663 (2019; Zbl 1472.03034)
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