Proof Theory and Ordered Groups
Logic
2017-08-03 v1
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 (l-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 l-groups is generated using an ordering theorem for abelian groups; a calculus is generated for l-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 l-groups is generated and a new proof is obtained that free groups are orderable.
Cite
@article{arxiv.1708.00640,
title = {Proof Theory and Ordered Groups},
author = {Almudena Colacito and George Metcalfe},
journal= {arXiv preprint arXiv:1708.00640},
year = {2017}
}