Advanced Search

In this note we provide a direct and simple proof of a result previously obtained by Astier stating that the class of spaces of orderings for which the pp conjecture holds true is closed under sheaves over Boolean spaces.

In this paper we present a method of obtaining new examples of spaces of orderings by considering quotient structures of the space of orderings $(X_{\mathbb{Q}\left(x\right)},G_{\mathbb{Q}\left(x\right)})$ - it is, in general, nontrivial to determine whether, for a subgroup $G₀\subset G_{\mathbb{Q}\left(x\right)}$ the derived quotient structure $(X_{\mathbb{Q}\left(x\right)}{|}_{G₀},G₀)$ is a space of orderings, and we provide some insights into this problem. In particular, we show that if a quotient structure arising from a subgroup of index 2 is a space of orderings, then it necessarily is a profinite one.

We investigate quotient structures and quotient spaces of a space of orderings arising from subgroups of index two. We provide necessary and sufficient conditions for a quotient structure to be a quotient space that, among other things, depend on the stability index of the given space. The case of the space of orderings of the field ℚ(x) is particularly interesting, since then the theory developed simplifies significantly. A part of the theory firstly developed for quotients of index 2 generalizes...