Spaces of Orders
by
Valentina Harizanov
George Washington University

A left order on a magma is a linear ordering of its elements that is left-invariant under the magma operation. The set of all left orders on a magma forms a natural topological space. Together with Dabkowska, Dabkowski, Przytycki and Veve, we show that this space is compact. In some cases, this space forms Cantor set, which was first investigated by Sikora for countable abelian torsion-free groups of finite rank. Together with Dabkowska, Dabkowski and Togha, we also investigate computability theoretic properties of orders on countable groups, using Turing degrees as a complexity measure.

Date received: December 12, 2007