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Stable embeddedness in algebraically closed valued fields

  • E. Hrushovski (a1) and A. Tatarsky (a2)

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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[1] Z. Chatzidakis and E. Hrushovski , Model theory of difference fields (Appendix), Transactions of American Mathematical Society, vol. 351 (1999), no. 8, pp. 29973071.

[2] O. Endler , Valuation theory, Springer-Verlag, 1972.

[4] E. Hrushovski and A. Pillay , Groups definable in local fields and pseudo-finite fields, Israel Journal of Mathematics, vol. 85 (1994), pp. 203262.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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