2016/06/01 by A. M. W. Glass, Glass, A. M. W., John S. Wilson +1 · 1 citation
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR
paper · pdf · doi:10.48550/arxiv.1606.00312
23 pages, 0 figures
arxiv created 2016/06/01 · arxiv updated 2016/06/02
Let (Ω, ≤) be a totally ordered set. We prove that if \Aut(Ω,≤) is transitive and satisfies the same first-order sentences as \Aut(\RR,≤) (in the language of lattice-ordered groups) then Ω 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(Ω,≤).