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Quantifier elimination in separably closed fields of finite imperfectness degree
Published online by Cambridge University Press: 12 March 2014
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.
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- Copyright © Association for Symbolic Logic 1988
References
REFERENCES
[1]
Ershov, Yu. L., Fields with solvable theory, Soviet Mathematics Doklady, 8 (1967), pp. 575–576.Google Scholar
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Fried, M. and Jarden, M., Field arithmetics, Springer-Verlag, Berlin, 1986.CrossRefGoogle Scholar
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Srour, G., The independence relation in separably closed fields, this Journal, vol. 51 (1986), pp. 715–725.Google Scholar