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Preprint Number 1149

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1149. A. M. W. Glass and John S. Wilson
Recognizing the real line

Submission date: 25 January 2017


Let (Ω, ≤) be a totally ordered set. We prove that if Aut(Ω,≤) is transitive and satisfies the same first-order sentences as the automorphism group of the real line (in the language of groups) then Ω and the real line are isomorphic ordered sets. This improvement of a theorem of Gurevich and Holland is obtained as a consequence of a study of centralizers associated with certain transitive subgroups of Aut(Ω,≤).

Mathematics Subject Classification: 20B07, 06F15

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Full text arXiv 1701.07235: pdf, ps.

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