Submission date: 8 October 2010.

Abstract:

We address the question which structures occur as fixed structures of stable structures with a generic automorphism. Among others we give a Galois theoretic characterisation. As application we prove: Any pseudofinite field is the fixed field of some model of ACFA. Any one-free pseudo-differentially closed field of characteristic zero is the fixed field of some model of DCFA. Any one-free PAC field of finite degree of imperfection is the fixed field of some model of SCFA.

Mathematics Subject Classification: 03C98 (primary), 12H10 (secondary)

Keywords and phrases: model theory, difference algebra, pseudofinite field

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