Quantifier Elimination following Muchnik

Abstract

This paper describes a very simple (high school level) algorithm of quantifier elimination for real closed fields and algebraically closed fields following an idea of A. Muchnik. The algorithm essentially relies on intermediate value property, pseudo-euclidean division and sign change table for univariate polynomials over R. Surprisingly this algorithm exhibits some more general feature and it can be very naturally turned into an algorithm of quantifier elimination for algebraically closed fields too