On quotients of the space of orderings of the field $\mathbb Q(x)$

Tom 108 / 2016

Paweł Gładki, Bill Jacob Banach Center Publications 108 (2016), 63-84 MSC: Primary 11E10; Secondary 12D15. DOI: 10.4064/bc108-0-6


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.


  • Paweł GładkiInstitute of Mathematics
    University of Silesia
    Bankowa 14
    40-007 Katowice, Poland
    Department of Computer Science
    AGH University of Science and Technology
    Mickiewicza 30
    30-059 Kraków, Poland
  • Bill JacobDepartment of Mathematics
    University of California, Santa Barbara
    Santa Barbara, CA 93106, USA

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