Space of orders with finite Cantor-Bendixson rank

Abstract

The goal of this paper is to show the following result: For every integer $n\ge 2$ there is a countable orderable group such that its space of orders is countable and has Cantor-Bendixson rank $n$. We show this by explicitly constructing a family of orderable groups with the desired properties.

13 pages. Improved exposition in sections 4 and 5

References in corpus (2)

• The space of left orders of a group is either finite or uncountable
• Dense orderings in the space of left-orderings of a group