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Proof Theory and Ordered Groups

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Logic, Language, Information, and Computation (WoLLIC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10388))

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 (\(\ell \)-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.

Supported by Swiss National Science Foundation grant 200021_146748 and the EU Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 689176.

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Authors and Affiliations

  1. Mathematical Institute, University of Bern, Bern, Switzerland

    Almudena Colacito & George Metcalfe

Authors
  1. Almudena Colacito
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  2. George Metcalfe
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Correspondence to George Metcalfe .

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Editors and Affiliations

  1. Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland

    Juliette Kennedy

  2. Centro de Informática, Recife, Pernambuco, Brazil

    Ruy J.G.B. de Queiroz

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Colacito, A., Metcalfe, G. (2017). Proof Theory and Ordered Groups. In: Kennedy, J., de Queiroz, R. (eds) Logic, Language, Information, and Computation. WoLLIC 2017. Lecture Notes in Computer Science(), vol 10388. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55386-2_6

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  • DOI: https://doi.org/10.1007/978-3-662-55386-2_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-55385-5

  • Online ISBN: 978-3-662-55386-2

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