Bi-interpretable groups and lattices

Jambu-Giraudet, M.

doi:10.1090/S0002-9947-1983-0697073-2

Bi-interpretable groups and lattices
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Trans. Amer. Math. Soc. 278 (1983), 253-269 Request permission

Abstract:

A large class of $0\text {-}2$ 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.

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Lattice theory of some lattice-ordered groups

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On linearly ordered sets with

transitive groups of automorphisms

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