Generic automorphisms of fields Original Research Article

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 (via fixed fields) to Axʹs theory of pseudofinite fields, and analogues are obtained for most of Axʹs classical results. Some indication is given of the connection to nonstandard Frobenius maps.