The Journal of Symbolic Logic

Research Article

Stable embeddedness in algebraically closed valued fields

E. Hrushovskia1 * and A. Tatarskya2

a1 Department of Mathematics, Hebrew University, Jerusalem, Israel. E-mail: [email protected]

a2 Department of Mathematics, Hebrew University, Jerusalem, Israel. E-mail: [email protected]

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.

(Received April 11 2005)

Footnotes

*   Supported by Israel Science Foundation grant number 244/03