No positive cone in a free product is regular

@article{Hermiller2017NoPC,
  title={No positive cone in a free product is regular},
  author={Susan M. Hermiller and Zoran Sunic},
  journal={IJAC},
  year={2017},
  volume={27},
  pages={1113-1120}
}
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