Logic
The theory of closed ordered differential fields with m commuting derivations
Comptes Rendus. Mathématique, Volume 343 (2006) no. 3, pp. 151-154.

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:
Accepted:
Published online:
DOI: 10.1016/j.crma.2006.06.019
Rivière, Cédric 1

1 Université Denis-Diderot Paris 7, équipe de logique mathématique, 2, place Jussieu, 75251 Paris cedex 05, France
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Rivière, Cédric. 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. http://www.numdam.org/articles/10.1016/j.crma.2006.06.019/

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