Annals of Pure and Applied Logic 171 (6):102795 (2020)

This paper is devoted to understand groups definable in Presburger Arithmetic. We prove the following theorems: Theorem 1. Every group definable in a model of Presburger Arithmetic is abelian-by-finite. Theorem 2. Every bounded abelian group definable in a model of (Z, +, <) Presburger Arithmetic is definably isomorphic to (Z, +)^n mod out by a lattice.
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DOI 10.1016/j.apal.2020.102795
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