Proof theory for lattice-ordered groups

1 pages•Published: July 28, 2014

Abstract

Proof theory can provide useful tools for tackling problems in algebra. In particular, Gentzen systems admitting cut-elimination
have been used to establish decidability, complexity, amalgamation, admissibility, and generation results for varieties of residuated lattices corresponding to substructural logics. However, for classes of algebras bearing some family resemblance to groups, such as lattice-ordered groups, MV-algebras, BL-algebras, and cancellative residuated lattices, the proof-theoretic approach has met so far only with limited success.

The main aim of this talk will be to introduce proof-theoretic methods for the class of lattice-ordered groups and to explain how these methods can be used to obtain new syntactic proofs of two core theorems: namely, Holland's result that this class is generated as a variety by the lattice-ordered group of order-preserving automorphisms of the real numbers, and the decidability of the word problem for free lattice-ordered groups.

In: Nikolaos Galatos, Alexander Kurz and Constantine Tsinakis (editors). TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic, vol 25, pages 8.

Links:	https://easychair.org/publications/paper/BKGD
	https://doi.org/10.29007/3szk

BibTeX entry

@inproceedings{TACL2013:Proof_theory_lattice_ordered,
  author    = {George Metcalfe},
  title     = {Proof theory for lattice-ordered groups},
  booktitle = {TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic},
  editor    = {Nikolaos Galatos and Alexander Kurz and Constantine Tsinakis},
  series    = {EPiC Series in Computing},
  volume    = {25},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/BKGD},
  doi       = {10.29007/3szk},
  pages     = {8},
  year      = {2014}}

Download PDF Open PDF in browser