Proof Theory and Ordered Groups

Almudena Colacito; George Metcalfe

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arXiv · 1708.00640

Proof Theory and Ordered Groups

Almudena Colacito·George Metcalfe

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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.

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BibTeX RIS

Almudena Colacito, George Metcalfe. 2017-08-02. Proof Theory and Ordered Groups. https://arxiv.org/abs/1708.00640

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