Reverse mathematics and fully ordered groups

Abstract

We study theorems of ordered groups from the perspective of reverse mathematics. We show that RCA0 suffices to prove Hölder’s Theorem and give equivalences of both WKL0 (the orderability of torsion free nilpotent groups and direct products, the classical semigroup conditions for orderability) and ACA0 (the existence of induced partial orders in quotient groups, the existence of the center, and the existence of the strong divisible closure). © 1998 by the University of Notre Dame. All rights reserved.