  In this paper we present the following two results: we give an explicit
description of the space of orderings of the field Q(x) as an inverse limit of
finite spaces of orderings and we provide a new, simple proof of the fact that
the class of spaces of orderings for which the pp conjecture holds true is
closed under inverse limits. We discuss how these theorems interact with each
other, and explain our motivation to look into these problems.
