Existentially complete abelian lattice-ordered groups
Existentially complete abelian lattice-ordered groups
The theory of abelian totally ordered groups has a model completion. We show that the theory of abelian lattice-ordered groups has no model companion. Indeed, the Archimedean property can be captured by a first order $\forall \exists \forall$ sentence for existentially complete abelian lattice-ordered groups, and distinguishes between finitely generic …