Axiomatization of local-global principles for pp-formulas in spaces of orderings

Two important results in quadratic form theory, Pfister’s local-global principle and the isotropy theorem (see [5]), can be stated more generally for spaces of orderings (an abstract version of real spectras of formally real fields), for which they are expressed as local-global principles: A property of quadratic forms (expressed as a so-called positive-primitive formula) holds if and only if it holds locally (at every single ordering for Pfister’s local-global principle, at every finite subspace for the isotropy theorem).