Let G be a group. G is right-orderable provided it admits a total order ≤ satisfying hg _(1) ≤ hg _(2 ) whenever g 1) ≤ g _(2) . G is orderable provided it admits a total order ≤ satisfying both: hg 1) ≤ hg _(2) whenever g _(1) ≤ g _(2) and g 1) h ≤ g 2) h whenever g _(1) ≤ g _(2). A classical result shows that free groups are orderable. In this paper, we prove that left-orderable groups and orderable groups are quasivarieties of groups both with undecidable theory. For orderable groups, we find an explicit set of universal axioms.
展开▼
