  We provide a pure algebraic version of the dynamical characterization of
Conrad's property. This approach allows dealing with general group actions on
totally ordered spaces. As an application, we give a new and somehow
constructive proof of a theorem first established by Linnell: an orderable
group having infinitely many orderings has uncountably many. This proof is
achieved by extending to uncountable orderable groups a result about orderings
which may be approximated by their conjugates. This last result is illustrated
by an example of an exotic ordering on the free group given in the Appendix.

Group Theory;Dynamical Systems