Submission date: 1 June 2016

Abstract:

Let (Ω, ≤) be a totally ordered set. We prove that if Aut(Ω, ≤) is transitive and satisfies the same first-order sentences as Aut(R,≤) (in the language of lattice-ordered groups) then Ω and R 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(Ω, ≤).

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Full text arXiv 1606.00312: pdf, ps.