Multi-dimensional interpretations of Presburger arithmetic in itself

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00536783" target="_blank" >RIV/67985840:_____/20:00536783 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1093/logcom/exaa050" target="_blank" >https://doi.org/10.1093/logcom/exaa050</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1093/logcom/exaa050" target="_blank" >10.1093/logcom/exaa050</a>

Result language
angličtina
Original language name
Multi-dimensional interpretations of Presburger arithmetic in itself
Original language description
Presburger arithmetic is the true theory of natural numbers with addition. We study interpretations of Presburger arithmetic in itself. The main result of this paper is that all self-interpretations are definably isomorphic to the trivial one. Here we consider interpretations that might be multi-dimensional. We note that this resolves a conjecture by Visser (1998, An overview of interpretability logic. Advances in Modal Logic, pp. 307–359). In order to prove the result, we show that all linear orderings that are interpretable in (N,+) are scattered orderings with the finite Hausdorff rank and that the ranks are bounded in the terms of the dimensions of the respective interpretations.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA19-05497S" target="_blank" >GA19-05497S: Complexity of mathematical proofs and structures</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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