Hostname: page-component-7b7567c8c-lpg2g Total loading time: 0 Render date: 2026-11-15T22:18:46.020Z Has data issue: false hasContentIssue false
  • English
  • Français

Every real closed field has an integer part

Published online by Cambridge University Press:  12 March 2014

M. H. Mourgues and
J. P. Ressayre
M. H. Mourgues
Affiliation:
Equipe De Logique U.A. 753, Universite De Paris7, 75251 Paris Cedex 05, France
Get accessRights & Permissions [Opens in a new window]

Abstract

Let us call an integer part of an ordered field any subring such that every element of the field lies at distance less than I from a unique element of the ring. We show that every real closed field has an integer part.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 58 , Issue 2 , June 1993, pp. 641 - 647
Copyright
Copyright © Association for Symbolic Logic 1993

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.)

Article purchase

Temporarily unavailable

References

REFERENCES

[0]Shepherdson, J. C., A nonstandard model for a free variable fragment of number theory, Bulletin de l'academic Polonaise des sciences, XII (1964), n°2, pp. 79–86.Google Scholar
[1]Boughattas, S., Résultats positifs et négatifs sur l'existence d'une partie entiè;re dans les corps ordonnés; C.R.A.S. 1991 and Résultats optimaux sur l'existence d'une partie entiè;re dans les corps ordonnés, this Journal, to appear.Google Scholar
[2]Kaplansky, I., Maximal fields with valuations, Duke Mathematical Journal, vol. 9 (1942), pp. 303–321.CrossRefGoogle Scholar
[3]Ribenboim, P., Théorie des valuation, Les presses de l'université de Montréal, Montréal, 1968.Google Scholar
[4]Delon, F., Indécidabilité de la théorie des paires immédiates de corps valués henseliens, this Journal, vol. 56 (1991), pp. 1236–1242.Google Scholar
[5]Delon, F., Quelques propriétés des corps valués en théories des modè;les, Thè;se d'état. Paris 7, 1982.Google Scholar
[6]Mourgues, M. H., Applications des corps de series formelles à l'étude des corps reels clos et des corps exponentiels, These, Université de Paris 7, Paris, 1992.Google Scholar
[7]Mourgues, M. H. and Ressayre, J. P., The transfinite version of Puiseux's theorem, with application to integer parts in real closed fields, Proceedings of the 1990 Association for Symbolic Logic european colloquium in Helsinki, (to appear).Google Scholar