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Stable embeddedness in algebraically closed valued fields

Published online by Cambridge University Press:  12 March 2014

E. Hrushovski  and
A. Tatarsky
E. Hrushovski
Affiliation:
Department of Mathematics, Hebrew University, Jerusalem, Israel.E-mail:[email protected]
A. Tatarsky
Affiliation:
Department of Mathematics, Hebrew University, Jerusalem, Israel.E-mail:[email protected]
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Abstract

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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 71 , Issue 3 , September 2006 , pp. 831 - 862
Copyright
Copyright © Association for Symbolic Logic 2006

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References

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