Verdier stratifications and [wf]-stratification in o-minimal structures

Abstract

We prove the existence of Verdier stratifications for sets definable in any o-minimal structure on (R, +, .). It is also shown that the Verdier condition (w) implies the Whitney condition (b) in o-minimal structures on (R, +, .). As a consequence the Whitney Stratification Theorem holds. The existence of (wf)-stratification of functions definable in polynomially bounded o-minimal structures is presented.