# Proof Theory and Ordered Groups

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10388)

## Abstract

Ordering theorems, characterizing when partial orders of a group extend to total orders, are used to generate hypersequent calculi for varieties of lattice-ordered groups ($$\ell$$-groups). These calculi are then used to provide new proofs of theorems arising in the theory of ordered groups. More precisely: an analytic calculus for abelian $$\ell$$-groups is generated using an ordering theorem for abelian groups; a calculus is generated for $$\ell$$-groups and new decidability proofs are obtained for the equational theory of this variety and extending finite subsets of free groups to right orders; and a calculus for representable $$\ell$$-groups is generated and a new proof is obtained that free groups are orderable.

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