Journal of Symbolic Logic

Stable embeddedness in algebraically closed valued fields

E. Hrushovski and A. Tatarsky

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We give some general criteria for the stable embeddedness of a definable set. We use these criteria to establish the stable embeddedness in algebraically closed valued fields of two definable sets: The set of balls of a given radius r < 1 contained in the valuation ring and the set of balls of a given multiplicative radius r < 1. We also show that in an algebraically closed valued field a 0-definable set is stably embedded if and only if its algebraic closure is stably embedded.

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J. Symbolic Logic, Volume 71, Issue 3 (2006), 831-862.

First available in Project Euclid: 4 August 2006

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Hrushovski, E.; Tatarsky, A. Stable embeddedness in algebraically closed valued fields. J. Symbolic Logic 71 (2006), no. 3, 831--862. doi:10.2178/jsl/1154698580.

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