A constructive proof of Tarski's theorem on quantifier elimination in the theory of ACF
Grzegorz Pastuszak · arXiv (Cornell University) · 2016
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 $\\varphi$ of the language of fields we construct a quantifier-free formula $\\varphi'$ such that $ACF\\vdash\\varphi\\leftrightarrow\\varphi'$. We devote the last section of the paper to show some applications of this constructive version in mathematics and physics.