  We prove that there exists a functorial correspondence between MV-algebras
and partially cyclically ordered groups which are wound round of
lattice-ordered groups. It follows that some results about cyclically ordered
groups can be stated in terms of MV-algebras. For example, the study of groups
together with a cyclic order allows to get a first-order characterization of
groups of unimodular complex numbers and of finite cyclic groups. We deduce a
characterization of pseudofinite MV-chains and of pseudo-simple MV-chains (i.e.
which share the same first-order properties as some simple ones). We can
generalize these results to some non-lineraly ordered MV-algebras, for example
hyper-archimedean MV-algebras.
