%0 Journal Article %T The space of left orders of a group is either finite or uncountable %A Peter A. Linnell %J Mathematics %D 2009 %I arXiv %R 10.1112/blms/bdq099 %X 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 This paper retrieves correct parts of the withdrawn paper arXiv:math/0607470. %U http://arxiv.org/abs/0909.2497v1