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Proof theory and ordered groups. (English) Zbl 1496.03227

Kennedy, Juliette (ed.) et al., Logic, language, information, and computation. 24th international workshop, WoLLIC 2017, London, UK, July 18–21, 2017. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 10388, 80-91 (2017).
Summary: 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.
For the entire collection see [Zbl 1369.03021].

MSC:

03F03 Proof theory in general (including proof-theoretic semantics)
06F15 Ordered groups
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