Bi-orders do not arise from total orders

We present some Zermelo-Fraenkel consistency results regarding bi-orderability of groups, as well a construction groups with Conradian orders whose every action on metric spaces has bounded orbits. A classical consequence the ultrafilter lemma is that group bi-orderable if and only it locally bi-orderable. show there exists model ZF in which free (ergo bi-orderable) not bi-orderable, can be given total order. Such also exist presence principle dependent choices. Comparable are provided for torsion-free abelian groups.