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Définissabilité dans les corps de fonctions p-adiques

Published online by Cambridge University Press:  12 March 2014

Luc Bélair  and
Jean-Louis Duret
Luc Bélair
Affiliation:
Département de Mathématiques et Informatique, Université de Québec à Montréal, Montréal, Québec H3C 3P8, Canada
Jean-Louis Duret
Affiliation:
Faculté des Sciences, Université d'Angers, 49045 Angers, France Équipe de Logique Mathématique, Université Paris-VII, 75251 Paris, France
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Abstract

We study function fields over p-adically closed fields in the first-order language of fields. Using ideas of Duret [D], we show that the field of constants is definable, and that the genus is an elementary property.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 56 , Issue 3 , September 1991 , pp. 783 - 785
Copyright
Copyright © Association for Symbolic Logic 1991

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References

RÉFÉRENCES

[B] Bélair, L., Théorie des modèles des corps p-adiques, Séminaire de structures algébriques ordonnées, année 1985–1986 (Delon, F. et al., éditeurs), Université Paris-VII, Paris, 1986.Google Scholar
[D] Duret, J.-L., Sur la théorie élémentaire des corps de fonctions, ce Journal, vol. 51 (1986), pp. 948–956.Google Scholar
[H] Hasse, H., Number theory, Springer-Verlag, Berlin, 1980.CrossRefGoogle Scholar
[N] Narkiewicz, W., Elementary and analytic theory of algebraic numbers, PWN, Warsaw, 1974.Google Scholar