Proof Theory for Lattice-ordered Groups
College of Natural Science and Mathematics, Mathematics
Lattice-ordered groups, Proof theory, Hypersequent calculi, Cut elimination, Co-NP completeness
Proof-theoretic methods are developed and exploited to establish properties of the variety of lattice-ordered groups. In particular, a hypersequent calculus with a cut rule is used to provide an alternative syntactic proof of the generation of the variety by the lattice-ordered group of automorphisms of the real number chain. Completeness is also established for an analytic (cut-free) hypersequent calculus using cut elimination and it is proved that the equational theory of the variety is co-NP complete.
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Galatos, Nikolaos, and Metcalfe, George. “Proof Theory for Lattice-Ordered Groups.” Annals of Pure and Applied Logic, vol. 167, no. 8, 2016, pp. 707–724. doi: 10.1016/j.apal.2016.04.004.