Colacito, Almudena; Metcalfe, George
(2017).
*
Proof Theory and Ordered Groups.
*
In:
Kennedy, Juliette; de Queiroz, Ruy J.G.B.
(eds.)
Proceedings of WoLLIC 2017. Logic, Language, Information, and Computation. Lecture Notes in Computer Science: Vol. 10388 (pp. 80-91).
Springer-Verlag Berlin Heidelberg
10.1007/978-3-662-55386-2_6

Text
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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.

## Item Type: |
Book Section (Book Chapter) |
---|---|

## Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |

## UniBE Contributor: |
Colacito, Almudena and Metcalfe, George |

## Subjects: |
500 Science > 510 Mathematics |

## ISBN: |
978-3-662-55386-2 |

## Series: |
Lecture Notes in Computer Science |

## Publisher: |
Springer-Verlag Berlin Heidelberg |

## Language: |
English |

## Submitter: |
George Metcalfe |

## Date Deposited: |
18 Aug 2017 09:15 |

## Last Modified: |
18 Aug 2017 09:15 |

## Publisher DOI: |
10.1007/978-3-662-55386-2_6 |

## BORIS DOI: |
10.7892/boris.102029 |

## URI: |
https://boris.unibe.ch/id/eprint/102029 |