Hostname: page-component-6bb9c88b65-9rk55 Total loading time: 0 Render date: 2025-07-23T01:24:17.240Z Has data issue: false hasContentIssue false
  • English
  • Français

Small fields

Published online by Cambridge University Press:  12 March 2014

Frank O. Wagner
Frank O. Wagner*
Affiliation:
Mathematical Institute, 24-29 St Giles', Oxford OX1 3LB, England E-mail: wagner@maths.ox.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

An infinite field with only countably many pure types is algebraically closed.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 63 , Issue 3 , September 1998 , pp. 995 - 1002
Copyright
Copyright © Association for Symbolic Logic 1998

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

[1]Duret, Jean-Louis, Les corps algébriquement clos non séparablement clos ont la propriété d'indépendance, Model theory of algebra and arithmetic, Proc. Karpacz 1979 (Pacholski, L., Wierzejewski, J., and Wilkie, A. J., editors), Springer-Verlag, Berlin, New York, 1980, pp. 136–162.Google Scholar
[2]Lang, Serge, Algebra, Addison-Wesley, New York, 1965.Google Scholar
[3]Macintyre, Angus, The complexity of types infield theory, Proc. Logic Year 1979/80, University of Connecticut (Lerman, M., Schmerl, J. H., and Soare, R. I., editors), Springer-Verlag, Berlin, New York, 1981, pp. 141–156.Google Scholar
[4]Reineke, Joachim, Minimale Gruppen, Zeitschrift für Math. Logik, vol. 21 (1975), pp. 357–359.Google Scholar
[5]Wagner, Frank O., Small stable groups and generics, this Journal, vol. 56 (1991), pp. 1026–1037.Google Scholar