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The space of left orders of a group is either finite or uncountable.

Втр, 09/15/2009 - 11:27 — SomNambul
Authors: Peter A. Linnell
Subjects: Group Theory
link: http://arxiv.org/abs/0909.2497
Abstract

Let G be a group and let O_G denote the set of left orderings on G. Then O_G
can be topologized in a natural way, and we shall study this topology to show
that O_G can never be countably infinite. This paper retrieves correct parts of
the withdrawn paper arXiv:math/0607470.