In this paper we discuss the problem to carry over the well-known
Minkowski-Hasse local-global principle to the context of an infinite algebraic
extension of the rationals or the rational function fields Wq(x) over finite fields.
Applying this result we give a new proof of the elementary type conjecture for
Witt rings of infinite algebraic extensions of global fields. This generalizes a
result of I. Efrat [Ef] who proved, using Galois cohomology methods, a similar
fact for algebraic extensions of the rationals