On Marshall’s p-invariant for semianalytic set germs

Abstract

The invariant p(V ) has been introduced by M. Marshall as a measure of the complexity of semialgebraic sets of a real algebraic variety V . This invariant is defined as the least integer such that every semialgebraic set S ⊂ V has a separating family with p(V ) polynomials. In this paper we provide estimates for the invariant p in the case of analytic set germs. One of the tools we use is a realization theorem which is interesting by itself.