Signatures andS-discrete lattice-ordered groups

The central theme of this article is the approximation of lattice-ordered groups (l-groups) first by Specker groups and, subsequently, by the so-calledS-discretel-groups. The sense of these approximations is made precise via the notion of a signature, defined below, and by that ofa^*-subgroups.Sample result: ifG is a projectablel-group then it has anl-subgroupH which is Specker and for which the mapPPH defines a boolean isomorphism between the algebras of polars ofG andH.Presented by L. Fuchs.This article was written while this author was a Stouffer Visiting Professor at the University of Kansas. He wishes to thank the members of the Mathematics Department of that institution for their hospitality.