An expansion of abelian ℓ-groups with a spectral subspace map admits a model companion that is complete and has quantifier elimination.
Algebraically closed and existentially closed Abelian lattice-ordered groups
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A Model Companion for Abelian Lattice-Ordered Groups with a Valuation
An expansion of abelian ℓ-groups with a spectral subspace map admits a model companion that is complete and has quantifier elimination.