Hostname: page-component-7bb8b95d7b-dtkg6 Total loading time: 0 Render date: 2024-09-11T07:32:15.018Z Has data issue: false hasContentIssue false

Small fields

Published online by Cambridge University Press:  12 March 2014

Frank O. Wagner*
Affiliation:
Mathematical Institute, 24-29 St Giles', Oxford OX1 3LB, England E-mail: wagner@maths.ox.ac.uk

Abstract

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

Type
Research Article
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.)

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. 136162.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. 141156.Google Scholar
[4]Reineke, Joachim, Minimale Gruppen, Zeitschrift für Math. Logik, vol. 21 (1975), pp. 357359.Google Scholar
[5]Wagner, Frank O., Small stable groups and generics, this Journal, vol. 56 (1991), pp. 10261037.Google Scholar