Let (C,R) be the countable dense circular ordering, and G its automorphism group. It is shown that certain properties of group elements are first order definable in G, and these results are used to reconstruct C inside G, and to demonstrate that its outer automorphism group has order 2. Similar statements hold for the completion C̅.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm204-2-1,
author = {J. K. Truss},
title = {On the automorphism group of the countable dense circular order},
journal = {Fundamenta Mathematicae},
volume = {205},
year = {2009},
pages = {97-111},
zbl = {1174.06002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm204-2-1}
}
J. K. Truss. On the automorphism group of the countable dense circular order. Fundamenta Mathematicae, Tome 205 (2009) pp. 97-111. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm204-2-1/