No positive cone in a free product is regular

  title={No positive cone in a free product is regular},
  author={Susan M. Hermiller and Zoran Sunic},
We show that there exists no left order on the free product of two nontrivial, finitely generated, left-orderable groups such that the corresponding positive cone is represented by a regular language. Since there are orders on free groups of rank at least two with positive cone languages that are contextfree (in fact, 1-counter languages), our result… CONTINUE READING