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Verdier and strict Thom stratifications in o-minimal structures. (English) Zbl 0909.32008
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 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 C. Miller, Ann. Pure Appl. Logic 68, No. 1, 79-84 (1994; Zbl 0823.03018)].
Reviewer: Ta Lê Loi (Dalat)

##### MSC:
 32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects) 14P10 Semialgebraic sets and related spaces 14B05 Singularities in algebraic geometry