Interpreting formulas of divisible lattice ordered abelian groups

TL;DR

This paper demonstrates that a broad class of divisible lattice-ordered abelian groups of continuous functions can be interpreted within the lattice of their zero sets, leading to significant model-theoretic applications like decidability.

Contribution

It introduces a novel interpretability framework for divisible abelian -groups in the lattice of zero sets, advancing the understanding of their model theory.

Findings

Interpretability of divisible -groups in zero set lattices

Decidability results for these -groups

Applications to model theory of lattice-ordered groups

Abstract

We show that a large class of divisible abelian $\ell$-groups (lattice ordered groups) of continuous functions is interpretable (in a certain sense) in the lattice of the zero sets of these functions. This has various applications to the model theory of these $\ell$-groups, including decidability results.