In this paper we present a method of obtaining new examples of spaces of orderings by considering quotient structures of the space of orderings - it is, in general, nontrivial to determine whether, for a subgroup the derived quotient structure 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc108-0-6,
author = {Pawe\l\ G\l adki and Bill Jacob},
title = {On quotients of the space of orderings of the field $\mathbb{Q}$(x)},
journal = {Banach Center Publications},
volume = {108},
year = {2016},
pages = {63-84},
zbl = {06622286},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc108-0-6}
}
Paweł Gładki; Bill Jacob. On quotients of the space of orderings of the field ℚ(x). Banach Center Publications, Tome 108 (2016) pp. 63-84. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc108-0-6/