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.

• Type: Journal
• Year: 2008
• Where: JSYML
• Authors: Guillaume Valette
• Keywords: JSYML 2008, Metric Spaces, O-minimal Structure, Ominimal Structure