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

es 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). In his paper [7], Marshall introduces a much broader local-global principle that could be satisfied by spaces of orderings, and showed how several important questions about quadratic forms and real algebraic geometry would follow from it. He asks, for a space of orderings (X, G) (the unexplained terminology will be introduced later): "Is it true that any positive-primitive formula (

• Type: Journal
• Year: 2005
• Where: AML
• Authors: Vincent Astier, Marcus Tressl
• Keywords: AML 2005, Finite Subspace, Local-global Principle, Quadratic Forms