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Interpretations of Linear Orderings in Presburger Arithmetic

2019/11/17 by Alexander Zapryagaev, Zapryagaev, Alexander
Computer Science · #Advanced Algebra and Logic #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1911.07182

openalex publication_date 2019/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Presburger Arithmetic \mathopPrA\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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