Basicness of semialgebraic sets
A semialgebraic subset in a real algebraic variety is called basic if it is the set of solutions to a system of polynomial inequalities. The main result of the paper is that the basicness of semialgebraic sets on an affine variety defined over the field of real algebraic numbers is decidable. Another result is an explicit recursive decision procedure for basicness, each time splitting the original problem to a finite number of similar ones in one dimension less by desingularizing the ambient variety and the boundary of the semialgebraic set and passing to this boundary.
scientific article; zbMATH DE number 1384282