Bi-interpretable groups and lattices
Michèle Jambu-Giraudet · Transactions of the American Mathematical Society · 1983
A large class of 0 - 2 0\text {-}2 transitive lattice-ordered groups is finitely axiomatizable as a class of groups and as a class of lattices. In each model, the group structure and the lattice structure plus one parameter are bi-interpretable, sometimes up to duality only. A characterization of lattice-automorphisms of the structures is also given.