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

Published online by Cambridge University Press:  12 March 2014

Guillaume Valette
Guillaume Valette*
Affiliation:
Instytut Matematyki, Uniwersytet Jagielloński, UL. Reymonta 4, 30-059 Kraków, Poland, E-mail: Guillaume.Valette@im.uj.edu.pl
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 73 , Issue 2 , June 2008 , pp. 439 - 447
Copyright
Copyright © Association for Symbolic Logic 2008

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References

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