Proof Theory for Lattice-ordered Groups

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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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