A semialgebraic set is a subset of 
which is a finite Boolean combination of sets of
the form 
and 
,
where 
and 
are polynomials in 
,
..., 
over the reals.
By Tarski's theorem, the solution set of a quantified system of real algebraic equations and inequalities is a semialgebraic set (Strzebonski 2000).
