Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quotients of index two and general quotients in a space of orderings   In our work 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 in an elegant way to
quotients of index 2^n for arbitrary finite n. Numerous examples are provided.

18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int