 
Summary: Axiomatization of localglobal principles for
ppformulas in spaces of orderings
V. Astier, M. Tressl
Two important results in quadratic form theory, Pfister's localglobal
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 localglobal principles:
A property of quadratic forms (expressed as a socalled positiveprimitive
formula) holds if and only if it holds locally (at every single ordering for Pfis
ter's localglobal principle, at every finite subspace for the isotropy theorem).
In his paper [7], Marshall introduces a much broader localglobal principle
that could be satisfied by spaces of orderings, and showed how several im
portant 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 positiveprimitive formula (Żg) with
parameters Żg in G which holds in every finite subspace
of (X, G) necessarily holds in (X, G)?"
(LG)
No counterexamples are known. In this paper we work in the theory of
