The theory of closed ordered differential fields with <i>m</i> commuting derivations

Cédric Rivière

doi:10.1016/j.crma.2006.06.019

Logic

The theory of closed ordered differential fields with m commuting derivations

Presented by: Jean-Yves Girard

Cédric Rivière ¹

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

Comptes Rendus. Mathématique, Volume 343 (2006) no. 3, pp. 151-154.

Abstract
Résumé

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.

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 l'élimination des quantificateurs dans le langage naturel des anneaux ordonnés différentiels.

Received: 2006-06-06
Accepted: 2006-06-13
Published online: 2006-07-07

DOI: 10.1016/j.crma.2006.06.019

Author's affiliations:

Cédric Rivière ¹

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

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     title = {The theory of closed ordered differential fields with \protect\emph{m} commuting derivations},
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Cédric Rivière. The theory of closed ordered differential fields with m commuting derivations. Comptes Rendus. Mathématique, Volume 343 (2006) no. 3, pp. 151-154. doi : 10.1016/j.crma.2006.06.019. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.06.019/

References
Cited by

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[4] L. van den Dries; K. Schmidt Bounds in the theory of polynomials rings over fields. A nonstandard approach, Invent. Math., Volume 76 (1984), pp. 77-91

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