Generic automorphisms of fields

Annals of Pure and Applied Logic 88 (2):165-180 (1997)
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Abstract

It is shown that the theory of fields with an automorphism has a decidable model companion. Quantifier-elimination is established in a natural language. The theory is intimately connected to Ax's theory of pseudofinite fields, and analogues are obtained for most of Ax's classical results. Some indication is given of the connection to nonstandard Frobenius maps

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10.1016/s0168-0072(97)00020-1

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Citations of this work

Existentially closed fields with finite group actions.Daniel M. Hoffmann & Piotr Kowalski - 2018 - Journal of Mathematical Logic 18 (1):1850003.
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Galois stratification and ACFA.Ivan Tomašić - 2015 - Annals of Pure and Applied Logic 166 (5):639-663.
Fields with several commuting derivations.David Pierce - 2014 - Journal of Symbolic Logic 79 (1):1-19.

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References found in this work

Existentially closed structures.H. Simmons - 1972 - Journal of Symbolic Logic 37 (2):293-310.
The Elementary Theory of Finite Fields.James Ax - 1973 - Journal of Symbolic Logic 38 (1):162-163.

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