Quotients of Index Two and General Quotients in a Space of Orderings

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Date
2011-05-30MFO Scientific Program
Research in Pairs 2011Series
Oberwolfach Preprints;2011,36Author
Gladki, Pawel
Marshall, Murray
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Abstract
In this paper 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 important, since then the theory developed simplifies significantly. A part of the theory firstly developed for quotients of index $2$ generalizes in an elegant way to quotients of index $2^n$ for arbitrary finite n. Numerous examples are provided.