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On metric types that are definable in an o-minimal structure

  • Guillaume Valette (a1)


In this paper we study the metric spaces that are definable in a polynomially bounded o-minimal structure. We prove that the family of metric spaces definable in a given polynomially bounded o-minimal structure is characterized by the valuation field Λ of the structure. In the last section we prove that the cardinality of this family is that of Λ. In particular these two results answer a conjecture given in [SS] about the countability of the metric types of analytic germs. The proof is a mixture of geometry and model theory.



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[V2]Valette, G., Lipschitz triangulations, Illinois Journal of Mathematics, to appear.

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On metric types that are definable in an o-minimal structure

  • Guillaume Valette (a1)


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