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Interpretations of Presburger Arithmetic in Itself

Authors :
Zapryagaev, Alexander
Pakhomov, Fedor
Publication Year :
2017

Abstract

Presburger arithmetic PrA is the true theory of natural numbers with addition. We study interpretations of PrA in itself. We prove that all one-dimensional self-interpretations are definably isomorphic to the identity self-interpretation. In order to prove the results we show that all linear orders that are interpretable in (N,+) are scattered orders with the finite Hausdorff rank and that the ranks are bounded in terms of the dimension of the respective interpretations. From our result about self-interpretations of PrA it follows that PrA isn't one-dimensionally interpretable in any of its finite subtheories. We note that the latter was conjectured by A. Visser.<br />Comment: Published in proceedings of LFCS 2018

Subjects

Subjects :
Mathematics - Logic
03C40

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.1709.07341
Document Type :
Working Paper