Open Questions in The Theory of Spaces of Orderings

Spaces of orderings provide an abstract framework in which to study spaces of orderings of formally real fields. Spaces of orderings of finite chain length are well understood [9] [12]. The Isotropy Theorem [12] and the extension of the Isotropy Theorem given in [13] are the main tools for reducing questions to the finite case, and these are quite effective. At the same time, there are many questions which do not appear to reduce in this way. In this paper we consider four such questions, for a space of orderings (X,G).