Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-28T01:10:48.455Z Has data issue: false hasContentIssue false
  • English
  • Français

Corps portant un nombre fini de valuations

Published online by Cambridge University Press:  12 March 2014

Françoise Delon
Françoise Delon*
Affiliation:
U.E.R. de Mathématique et Informatique, Université Paris VII, 75251 Paris Cédex 05, France
Get access Rights & Permissions [Opens in a new window]

Abstract

L. van den Dries proved that the theory of n-valued rings has a model companion. We show here that this result is still true when the valuation rings are required to satisfy given inclusion relations (we restrict ourselves to the case of residual characteristic zero).

Keywords

Primary 03C60Ax-Kochen-Eršov theoremmodel companionn-valued ringvan den Dries's theory
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 52 , Issue 4 , December 1987 , pp. 994 - 1004
Copyright
Copyright © Association for Symbolic Logic 1987

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

RÉFÉRENCES

[D]Delon, F., Élimination des quantificateurs dans les corps valués (en préparation).Google Scholar
[E]Eršov, Ju. L., Multiply valued fields, Soviet Mathematics Doklady, vol. 22 (1980), pp. 63–66.Google Scholar
[Ka]Kaplansky, I., Maximal fields with valuations, Duke Mathematical Journal, vol. 9 (1942), pp. 303–321.CrossRefGoogle Scholar
[Ko]Kochen, S., The model theory of local fields, ⊨ ISILC logic conference (Kiel, 1974), Lecture Notes in Mathematics, vol. 499, Springer-Verlag, Berlin, 1975, pp. 384–425.CrossRefGoogle Scholar
[R]Ribenboim, P., Théorie des valuations, Les Presses de l'Université de Montréal, Montréal, 1964.Google Scholar
[vdD]van den Dries, L., Model theory of fields, Thèse, Université d'Utrecht, Utrecht, 1978.Google Scholar