On quotients of the space of orderings of the field $\mathbb Q(x)$
Volume 108 / 2016
Banach Center Publications 108 (2016), 63-84
MSC: Primary 11E10; Secondary 12D15.
DOI: 10.4064/bc108-0-6
Abstract
In this paper we present a method of obtaining new examples of spaces of orderings by considering quotient structures of the space of orderings $(X_{\mathbb Q(x)}, G_{\mathbb Q(x)})$ — it is, in general, nontrivial to determine whether, for a subgroup $G_0 \subset G_{\mathbb Q(x)}$ the derived quotient structure $(X_{\mathbb Q(x)}|_{G_0}, G_0)$ 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.
