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JSYML
2008

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

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On metric types that are definable in an o-minimal structure
Abstract. In this paper we study the metric spaces that are definable in a polynomially bounded ominimal structure. We prove that the family of metric spaces definable in a given polynomially bounded o-minimal structure is characterized by the valuation field of the structure. In the last section we prove that the cardinality of this family is that of . 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.
Guillaume Valette
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2008
Where JSYML
Authors Guillaume Valette
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