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Quantified System


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

 QS=Q_1(y_1)Q_2(y_2)...Q_m(y_m)S(x_1,...,x_n;y_1,...,y_m),

where Q is a quantifier ( exists or  forall ) and S 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.


See also

Quantifier, Semialgebraic Set, Tarski's Theorem

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References

Strzebonski, A. "Solving Algebraic Inequalities." Mathematica J. 7, 525-541, 2000.

Referenced on Wolfram|Alpha

Quantified System

Cite this as:

Weisstein, Eric W. "Quantified System." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/QuantifiedSystem.html

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