Modèle complétude des structures o-minimales polynomialement bornées

Olivier Le Gal

doi:10.1016/j.crma.2007.10.049

Géométrie/Logique

Modèle complétude des structures o-minimales polynomialement bornées
[Model completeness in o-minimal polynomially bounded structures]

Presented by: Bernard Malgrange

Olivier Le Gal ¹

¹ IRMAR, Campus de Beaulieu, 35042 Rennes cedex, France

Comptes Rendus. Mathématique, Volume 346 (2008) no. 1-2, pp. 59-62.

Abstract
Résumé

We show an explicit theorem of the complement “Gabrielov's '96 like” for o-minimal polynomially bounded structures. In model theoretic terms, this is equivalent to the model completeness of $〈 R, >, +, *, F 〉$ where $F$ is a global differential algebra of maps definable in an o-minimal polynomially bounded structure.

On montre un théorème du complémentaire explicite « à la Gabrielov '96 » dans les structures o-minimales polynomialement bornées. Cette propriété équivaut à la modèle complétude de la structure $〈 R, >, +, *, F 〉$ , où $F$ est une algèbre différentielle globale d'applications définissables dans une structure o-minimale polynomialement bornée.

Received: 2006-10-25
Accepted: 2007-10-30
Published online: 2007-12-03

DOI: 10.1016/j.crma.2007.10.049

Author's affiliations:

Olivier Le Gal ¹

¹ IRMAR, Campus de Beaulieu, 35042 Rennes cedex, France

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     title = {Mod\`ele compl\'etude des structures o-minimales polynomialement born\'ees},
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Olivier Le Gal. Modèle complétude des structures o-minimales polynomialement bornées. Comptes Rendus. Mathématique, Volume 346 (2008) no. 1-2, pp. 59-62. doi : 10.1016/j.crma.2007.10.049. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.10.049/

References
Cited by

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[9] A. Wilkie A theorem of the complement and some new o-minimal structures, Sel. Math., Volume 5 (1999), pp. 397-421

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