Journal of Symbolic Logic

On algebraic closure in pseudofinite fields

Özlem Beyarslan and Ehud Hrushovski

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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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J. Symbolic Logic Volume 77, Issue 4 (2012), 1057-1066.

First available in Project Euclid: 15 October 2012

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Beyarslan, Özlem; Hrushovski, Ehud. On algebraic closure in pseudofinite fields. J. Symbolic Logic 77 (2012), no. 4, 1057--1066. doi:10.2178/jsl.7704010.

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