Submission date: 1 September 2006

Abstract:

In "Pseudo-finite fields and related structures" Hrushovski asks (in a more general context) whether the notion of measure on definable sets in pseudo-finite fields can be extended to perfect PAC fields whose Galois group is bounded but not \hat{\Z} (the profinite completion of the integers). We define a suitable generalization of measure and give an answer to this question: yes if the Galois group is pro-cyclic, no otherwise.

Mathematics Subject Classification: 03C60, 12L12, 12E30, 12F10

Keywords and phrases : pseudo-algebraically closed fields, measure, definable sets, bounded Galois group,

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