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June 2008 On metric types that are definable in an o-minimal structure
Guillaume Valette
J. Symbolic Logic 73(2): 439-447 (June 2008). DOI: 10.2178/jsl/1208359053

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.

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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

Information

Published: June 2008
First available in Project Euclid: 16 April 2008

zbMATH: 1145.03017
MathSciNet: MR2414458
Digital Object Identifier: 10.2178/jsl/1208359053

Subjects:
Primary: 03C64, 14P15

Rights: Copyright © 2008 Association for Symbolic Logic

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Vol.73 • No. 2 • June 2008
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