Linear orders in Presburger arithmetic
Fedor Nikolaevich Pakhomov, Alexander Zapryagaev · Logic Journal of IGPL · 2026
Abstract We prove the linear orders first-order definable in the standard model $(\mathbb{Z};<,+)$ of Presburger arithmetic are exactly those that are $(\mathbb{Z};<,+)$-definably embeddable into the lexicographic ordering on $\mathbb{Z}^{n}$ for some $n$.