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arXiv:1701.07235 [math.GR]AbstractReferencesReviewsResources

Recognizing the real line

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

Published 2017-01-25Version 1

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 the automorphism group of the real line (in the language of groups) then $\Omega$ and 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$(\Omega,\leq)$.

Comments: 13 pages. arXiv admin note: substantial text overlap with arXiv:1606.00312
Categories: math.GR
Subjects: 20B07, 06F15
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