A constructive proof of Tarski's theorem on quantifier elimination in the theory of ACF
Abstract
Assume that ACF denotes the theory of algebraically closed fields. The renowned theorem of A. Tarski states that ACF admits quantifier elimination. In this paper we give a constructive proof of Tarski's theorem on quantifier elimination in ACF. This means that for a given formula of the language of fields we construct a quantifier-free formula ' such that ACF'. We devote the last section of the paper to show some applications of this constructive version in mathematics and physics.
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