Verdier and strict Thom stratifications in o-minimal structures
We prove the existence of Verdier stratifications for sets definable in any \(o\)-minimal structure on \((\mathbb{R},+, \cdot)\) [for the definition of \(o\)-minimal structures see \textit{L. van den Dries}, `Tame topology and \(O\)-minimal structures, Cambridge University Press (1997)]. It is also shown that the Verdier condition \((w)\) implies the Whitney condition (b) in \(o\)-minimal structures on \((\mathbb{R},+, \cdot)\). We establish the existence of \((w_f)\)-stratification of functions definable in polynomially bounded \(o\)-minimal structures [for the definition, see \textit{C. Miller}, Ann. Pure Appl. Logic 68, No. 1, 79-84 (1994; Zbl 0823.03018)].
scientific article; zbMATH DE number 1191166