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Nous donnons une nouvelle démonstration d'un théorème de Cano-Lion-Moussu: la frontière d'une hypersurface pfaffienne non spiralante est une réunion localement finie de sous-variétés analytiques connexes.
Nous donnons une preuve géométrique du théorème d’élimination des quantificateurs pour les fonctions logarithmico-exponentielles prouvé initialement par van den Dries, Macintyre et Marker. Notre démonstration n’utilise pas de Théorie des Modèles. Elle repose sur un théorème de préparation pour les fonctions sous-analytiques.
Un sous-ensemble pfaffien d’un ouvert semi-analytique est une intersection finie d’ensembles semi-analytiques relativement compacts de et de feuilles non spiralantes de certains feuilletages analytiques de codimension 1 de Les sous-ensembles semi-pfaffiens de sont les éléments de la plus petite classe de sous-ensembles de contenant les sous-ensembles pfaffiens de , stable par intersection finie, réunion finie et différence symétrique. Les ensembles -pfaffiens sont les éléments de la...
Soit une fonction sous-analytique de à valeurs dans Nous montrons que l’intégrale est une fonction log-analytique de Nous en déduisons que le volume -dimensionnel des éléments d’une famille sous-analytique de sous-ensembles sous-analytiques globaux de l’espace euclidien est une fonction log-analytique de Un corollaire de ce résultat est le caractère log-analytique de la fonction densité -dimensionnelle d’un sous-analytique global de dimension en tout point de sa fermeture topologique....
We present an example of an o-minimal structure which does not admit cellular decomposition. To this end, we construct a function whose germ at the origin admits a representative for each integer , but no representative. A number theoretic condition on the coefficients of the Taylor series of then insures the quasianalyticity of some differential algebras induced by . The o-minimality of the structure generated by is deduced from this quasianalyticity property.
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