We show that the restriction of the Dehornoy ordering to an appropriate free subgroup of B3 defines a left ordering of the free group on k generators, k > 1, that has no convex subgroups. A group G is said to be left-orderable if there exists a strict total ordering of its elements such that g < h implies fg < fh for all f, g, h in G. To each left ordering < of a group G, we can associate the s...
