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Working paper

Interpretations of Linear Orderings in Presburger Arithmetic

math. arxive. Cornell University, 2019. No. 1911.07182.
Presburger Arithmetic PrA is the true theory of natural numbers with addition. We consider linear orderings interpretable in Presburger Arithmetic and establish various necessary and sucient 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.