English

Recognizing the real line

Group Theory 2017-01-26 v1

Abstract

Let (Ω,)(\Omega, \leq) be a totally ordered set. We prove that if Aut(Ω,)(\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 Ω\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(Ω,)(\Omega,\leq).

Keywords

Cite

@article{arxiv.1701.07235,
  title  = {Recognizing the real line},
  author = {A. M. W. Glass and John S. Wilson},
  journal= {arXiv preprint arXiv:1701.07235},
  year   = {2017}
}

Comments

13 pages. arXiv admin note: substantial text overlap with arXiv:1606.00312

R2 v1 2026-06-22T17:59:43.664Z