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arXiv · 1806.00315

Expansion of Presburger arithmetic with the exchange property

Nathanaël Mariaule
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Abstract

Let $G$ be a model of Presburger arithmetic. Let $\mathcal{L}$ be an expansion of the language of Presburger $\mathcal{L}_{Pres}$. In this paper we prove that the $\mathcal{L}$-theory of $G$ is $\mathcal{L}_{Pres}$-minimal iff it has the exchange property and any bounded definable set has a maximum.

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Nathanaël Mariaule. 2018-06-01. Expansion of Presburger arithmetic with the exchange property. https://arxiv.org/abs/1806.00315

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