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Paires élémentaires de corps pseudo-finis: dénombrement des complétions (Elementary pairs of pseudo-finite fields: counting completions)

Published online by Cambridge University Press:  12 March 2014

Hélène Lejeune
Hélène Lejeune*
Affiliation:
11 Rue F.J. Bouille, 92 260 Fontenay-Aux-Roses, France
*
Current address: 2 ruelle S' Pierre, 91 590 Cerny, France, E-mail: [email protected]
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Abstract

Let Π be a complete théorie of pseudo-finite fields. In this article we prove that, in the langage of fields to which we add a unary predicate for a substructure, the theory of non trivial elementary pairs of models of Π has completions, that is, the maximum that could exist.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 2 , June 2000 , pp. 705 - 718
Copyright
Copyright © Association for Symbolic Logic 2000

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References

REFERENCES

[1]Ax, J., The elementary theory of finite fields, Annals of Math, vol. 88 (1968), pp. 239–271.CrossRefGoogle Scholar
[2]Bousearen, E. and Poizat, B., Des belles paires aux beaux uples, this Journal, vol. 53 (1988), pp. 434–442.Google Scholar
[3]Fried, D. and Jarden, M., Field Arithmetic, Springer Verlag, Berlin, 1986.CrossRefGoogle Scholar
[4]Lejeune, H., Paires de corps PAC. parfaits, paires de corps pseudo-finis, th se de l'universit Paris 7, 1995.Google Scholar
[5]Seitenov, S. M., Theory of finite fields with an additional predicate distinguishing a subfield, Siberian Mathematical Journal, vol. 19 (1978), pp. 278–285.CrossRefGoogle Scholar