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# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## Quotients of index two and general quotients in a space of orderings

### Tom 229 / 2015

Fundamenta Mathematicae 229 (2015), 255-275 MSC: Primary 11E10; Secondary 12D15. DOI: 10.4064/fm229-3-3

#### Streszczenie

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 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 $2^n$ for arbitrary finite $n$. Numerous examples are provided.

#### Autorzy

University of Silesia
Bankowa 14
40-007 Katowice, Poland
and
Department of Computer Science
AGH University of Science and Technology
al. Mickiewicza 30
30-059 Kraków, Poland
e-mail
• Murray MarshallDepartment of Mathematics and Statistics