Systems of real varieties (Q1061183)

This paper gives a geometric interpretation of orderings of higher level of a function field F/\({\mathbb{R}}\). Further, it provides a stronger form of the local-global principle for weakly isotropic forms (Bröcker, Prestel) using only prime divisors of F/\({\mathbb{R}}\). Proofs are contained in the author's paper ''Prime divisors on real varieties and valuation theory'' (J. Algebra, to appear).