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Quantifier elimination in separably closed fields of finite imperfectness degree

Published online by Cambridge University Press:  12 March 2014

Dan Haran
Dan Haran*
Affiliation:
School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Ramat-Aviv, Tel-Aviv, Israel
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Extract

The theory of separably closed fields of a fixed characteristic and a fixed imperfectness degree is clearly recursively axiomatizable. Ershov [1] showed that it is complete, and therefore decidable. Later it became clear that this theory also has the prime extension property in a suitable language (cf. [4, Proposition 1]); hence it admits quantifier elimination. The purpose of this work is to give an explicit, primitive recursive procedure for such quantifier elimination in the case of a finite imperfectness degree.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 53 , Issue 2 , June 1988 , pp. 463 - 469
Copyright
Copyright © Association for Symbolic Logic 1988

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References

REFERENCES

[1] Ershov, Yu. L., Fields with solvable theory, Soviet Mathematics Doklady, 8 (1967), pp. 575–576.Google Scholar
[2] Fried, M., Haran, D. and Jarden, M., Galois stratification over Frobenius fields, Advances in Mathematics, vol. 51 (1984), pp. 1–35.CrossRefGoogle Scholar
[3] Fried, M. and Jarden, M., Field arithmetics, Springer-Verlag, Berlin, 1986.CrossRefGoogle Scholar
[4] Srour, G., The independence relation in separably closed fields, this Journal, vol. 51 (1986), pp. 715–725.Google Scholar
[5] Lang, S., Algebra, 2nd ed., Addison-Wesley, Reading, Massachusetts, 1984.Google Scholar