Quantified System

A quantified system of real algebraic equations and inequalities in variables ${x_1,...,x_n}$ is an expression

where is a quantifier ( or ) and is a system of real algebraic equations and inequalities in ${x_1,...,x_n;y_1,...,y_m}$ . By Tarski's theorem, the solution set of a quantified system of real algebraic equations and inequalities is a semialgebraic set.

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