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Comptes Rendus Mathématique
Volume 343, n° 3
pages 151-154 (août 2006)
Doi : 10.1016/j.crma.2006.06.019
Received : 6 June 2006 ;  accepted : 13 June 2006
The theory of closed ordered differential fields with m commuting derivations
La théorie des corps ordonnés différentiellement clos munis de m dérivations commutant entre elles
 

Cédric Rivière 1
Université Denis-Diderot Paris 7, équipe de logique mathématique, 2, place Jussieu, 75251 Paris cedex 05, France 

Abstract

We generalize the work of M. Singer (1978) on the theory of closed ordered differential fields to the case of m -ODF, the theory of ordered fields equipped with m commuting derivations. We give an algebraic axiomatization of the model completion (denoted by m -CODF) of this theory and we can immediately deduce that m -CODF has quantifier elimination in the natural language of ordered δ -rings. To cite this article: C. Rivière, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

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Résumé

Nous généralisons les travaux de M. Singer concernant la théorie des corps ordonnés différentiellement clos au cas des corps ordonnés munis de m dérivations commutant entre elles. Nous donnons une axiomatisation algébrique de la modèle-complétion de cette théorie et nous pouvons directement déduire que cette dernière admet lʼélimination des quantificateurs dans le langage naturel des anneaux ordonnés différentiels. Pour citer cet article : C. Rivière, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

The full text of this article is available in PDF format.
1  The author was supported by a FRIA grant during his PhD thesis at the University of Mons-Hainaut and is now supported by a MODNET grant.


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