Recognizing the real line
Group Theory
2017-01-26 v1
Abstract
Let be a totally ordered set. We prove that if Aut is transitive and satisfies the same first-order sentences as the automorphism group of the real line (in the language of groups) then 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.
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