The first-order theory of $\ell$-permutation groups

A. M. W. Glass; John S. Wilson

The first-order theory of $\ell$-permutation groups

Group Theory 2016-06-02 v1

Authors: A. M. W. Glass , John S. Wilson

Abstract

Let $(\Omega, \leq)$ be a totally ordered set. We prove that if $\Aut(\Omega,\leq)$ is transitive and satisfies the same first-order sentences as $\Aut(\RR,\leq)$ (in the language of lattice-ordered groups) then $\Omega$ and $\RR$ are isomorphic ordered sets. This improvement of a theorem of Gurevich and Holland is obtained as one of many consequences of a study of centralizers and coloured chains associated with certain transitive subgroups of $\Aut(\Omega,\leq)$ .

Keywords

permutation groups partially ordered sets

Cite

@article{arxiv.1606.00312,
  title  = {The first-order theory of $\ell$-permutation groups},
  author = {A. M. W. Glass and John S. Wilson},
  journal= {arXiv preprint arXiv:1606.00312},
  year   = {2016}
}

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23 pages, 0 figures

The first-order theory of $\ell$-permutation groups

Abstract

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