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arXiv · 1911.07182

Interpretations of Linear Orderings in Presburger Arithmetic

Alexander Zapryagaev
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Abstract

Presburger Arithmetic $\mathop{\mathbf{PrA}}\nolimits$ is the true theory of natural numbers with addition. We consider linear orderings interpretable in Presburger Arithmetic and establish various necessary and sufficient conditions for interpretability depending on dimension $n$ of interpretation. We note this problem is relevant to the interpretations of Presburger Arithmetic in itself, as well as the characterization of automatic orderings. For $n=2$ we obtain the complete criterion of interpretability.

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Alexander Zapryagaev. 2019-11-17. Interpretations of Linear Orderings in Presburger Arithmetic. https://arxiv.org/abs/1911.07182

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