Abstract
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.
Citation
Guillaume Valette. "On metric types that are definable in an o-minimal structure." J. Symbolic Logic 73 (2) 439 - 447, June 2008. https://doi.org/10.2178/jsl/1208359053
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