Minimal generation of basic semialgebraic sets (Q1066218)

If R denotes a real closed field and V an affine R-variety such that the rational points are dense in V, the author announces a bound, depending only on dim V, of the minimal m needed to describe a set of the form \(\{x\in V(R)| f_ i(x)>0,i=1,...,m\}\) where the \(f_ i\) are polynomial functions on V. The proof is only sketched.