no. 3
Logic
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]
Présenté par : Jean-Yves Girard
Rivière, Cédric1
1 Université Denis-Diderot Paris 7, équipe de logique mathématique, 2, place Jussieu, 75251 Paris cedex 05, France
Comptes Rendus. Mathématique, Tome 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.

Reçu le :
Accepté le :
Publié le :
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, Tome 343 (2006) no. 3, pp. 151-154. doi: 10.1016/j.crma.2006.06.019

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[2] Sacks, G. Saturated Model Theory, Benjamin, 1972

[3] Tressl, M. The uniform companion for large differential fields of characteristic zero, Trans. Amer. Math. Soc., Volume 357 (2005), pp. 3933-3951

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

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