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On algebraic closure in pseudofinite fields
Published online by Cambridge University Press: 12 March 2014
Abstract
We study the automorphism group of the algebraic closure of a substructure A of a pseudo-finite field F. We show that the behavior of this group, even when A is large, depends essentially on the roots of unity in F. For almost all completions of the theory of pseudofinite fields, we show that over A, algebraic closure agrees with definable closure, as soon as A contains the relative algebraic closure of the prime field.
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- Copyright © Association for Symbolic Logic 2012
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