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 to quotients of index 2ⁿ for arbitrary finite n. Numerous examples are provided.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm229-3-3,
author = {Pawe\l\ G\l adki and Murray Marshall},
title = {Quotients of index two and general quotients in a space of orderings},
journal = {Fundamenta Mathematicae},
volume = {228},
year = {2015},
pages = {255-275},
zbl = {06414106},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm229-3-3}
}
Paweł Gładki; Murray Marshall. Quotients of index two and general quotients in a space of orderings. Fundamenta Mathematicae, Tome 228 (2015) pp. 255-275. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm229-3-3/