Finitely Generic Abelian Lattice-Ordered Groups

Abstract

The authors characterize the finitely generic abelian lattice-ordered groups and make application of this characterization to specific examples.A key goal in Abraham Robinson's development of model-theoretic forcing was to explicate the notion of algebraically closed, even when the appropriate classes may not be first-order axiomatizable.Interesting links sometimes appear between purely algebraic properties and model-theoretic properties such as existentially closed (ex.) and finitely generic.In this spirit we consider the characterization of finitely generic abelian /-groups, as well as the model-theoretic properties of certain ex.abelian /-groups.The model theory of abehan lattice-ordered (/-) groups was developed by Glass and Pierce in [G-P] and [G-P2].They showed that every finitely generic structure is hyperarchimedean, and that the group C(X,R) is existentially closed.They also stated several problems, including:(i) Distinguish the finitely generic models among the hyperarchimedean ex.ones