Quotients of index two and general quotients in a space of orderings
Volume 229 / 2015
Fundamenta Mathematicae 229 (2015), 255-275
MSC: Primary 11E10; Secondary 12D15.
DOI: 10.4064/fm229-3-3
Abstract
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 ${\mathbb Q}(x)$ is particularly interesting, since then the theory developed simplifies significantly. A part of the theory firstly developed for quotients of index 2 generalizes to quotients of index $2^n$ for arbitrary finite $n$. Numerous examples are provided.
