Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-28T15:53:30.705Z Has data issue: false hasContentIssue false
  • English
  • Français

Indécidabilité de la théorie des paires immédiates de corps valués henseliens

Published online by Cambridge University Press:  12 March 2014

Françoise Delon
Françoise Delon*
Affiliation:
C.N.R.S. et U.F.R. de Mathématique et Informatique, Université Paris-VII, 75251 Paris, France
Get access Rights & Permissions [Opens in a new window]

Abstract

The theory of immediate pairs of Henselian valued fields, with a given residual theory (of characteristic zero) and a given theory of valuation group (nonzero), is undecidable and has completions.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 56 , Issue 4 , December 1991 , pp. 1236 - 1242
Copyright
Copyright © Association for Symbolic Logic 1991

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

[Bd]Baudisch, A., Theorien abelscher Gruppen mit einem einstelligen Prädikat, Fundamenta Mathematicae, vol. 83 (1974), pp. 121–127.CrossRefGoogle Scholar
[Br]. Baur, W., Die Theorie der Paare reell abgeschlossener Körper, Logic and algorithmic (papers from an international symposium in honor of Ernst Specker, Zurich, 1980), Monographies de l'Enseignement Mathématique, vol. 30, Université de Genève, Geneva, 1982, pp. 25–34.Google Scholar
[D1]Delon, F., Quelques propriétés des corps values en théorie des modèles, Thèse de Doctorat d'État, Université Paris-VII, Paris, 1982.Google Scholar
[D2]Delon, F., Extensions séparées et immédiates de corps valués, this Journal, vol. 53 (1988), pp. 421–428.Google Scholar
[FV]Feferman, S. and Vaught, R., The first order properties of products of algebraic systems, Fundamenta Mathematicae, vol. 47 (1959), pp. 57–103.CrossRefGoogle Scholar
[K]Kaplansky, I., Maximal fields with valuation, Duke Mathematical Journal, vol. 9 (1942), pp. 303–321.CrossRefGoogle Scholar
[L]Leloup, G., Théories complètes de paires de corps valués henseliens, this Journal, vol. 55 (1990), pp. 323–339.Google Scholar
[M]Macintyre, A., Classifying pairs of real closed fields, Ph.D. thesis, Stanford University, Stanford, California, 1967.Google Scholar
[R]Rogers, H., Certain logical reduction and decision problems, Annals of Mathematics, ser. 2, vol. 64 (1956), pp. 264–284.CrossRefGoogle Scholar
[Z]Zakon, E., Generalized Archimedean groups, Transactions of the American Mathematical Society, vol. 99 (1961), pp. 21–40.CrossRefGoogle Scholar