Analytic stratification in the Pfaffian closure of an \(o\)-minimal structure

DOI10.1215/S0012-7094-00-10322-5zbMath0970.32009MaRDI QIDQ1572887

Patrick Speissegger, Jean-Marie Lion

Publication date: 16 October 2001

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

cell decompositionPfaffian closureanalytic stratification\(o\)-minimal structure

Mathematics Subject Classification ID

Pfaffian systems (58A17) Semi-analytic sets, subanalytic sets, and generalizations (32B20) Applications of model theory (03C98)

Related Items (11)

Topological types of Pfaffian manifolds ⋮ The theorem of the complement for nested sub-Pfaffian sets ⋮ Zero sets of smooth functions in the Pfaffian closure of an o-minimal structure ⋮ On smooth locally o-minimal functions ⋮ Pfaffian Sets and O-minimality ⋮ Definability in o-minimal expansions of the real numbers ⋮ Smooth functions in o-minimal structures ⋮ First order tameness of measures ⋮ Tame flows ⋮ o-minimal analytic separation of sets in dimension 2 ⋮ Differential equations over polynomially bounded o-minimal structures

Cites Work

• \(p\)-adic and real subanalytic sets
• Convergence of the multilevel full approximation scheme including the V- cycle
• The theory of Khovanskii and the problem of Dulac.
• Volumes, Rolle leaves of analytic foliations and Wilkie's theorem
• Geometric categories and o-minimal structures
• Projections of semi-analytic sets
• Partial Differential Relations
• The Pfaffian closure of an o-minimal structure
• Definable types in -minimal theories
• T-convexity and tame extensions II
• Frontière d'une hypersurface pfaffienne
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