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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

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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