## Notre Dame Journal of Formal Logic

### On Interpretability in the Theory of Concatenation

Vítězslav Švejdar

#### Abstract

We prove that a variant of Robinson arithmetic $\mathsf{Q}$ with nontotal operations is interpretable in the theory of concatenation $\mathsf{TC}$ introduced by A. Grzegorczyk. Since $\mathsf{Q}$ is known to be interpretable in that nontotal variant, our result gives a positive answer to the problem whether $\mathsf{Q}$ is interpretable in $\mathsf{TC}$. An immediate consequence is essential undecidability of $\mathsf{TC}$.

#### Article information

Source
Notre Dame J. Formal Logic Volume 50, Number 1 (2009), 87-95.

Dates
First available in Project Euclid: 19 January 2009

https://projecteuclid.org/euclid.ndjfl/1232375164

Digital Object Identifier
doi:10.1215/00294527-2008-029

Mathematical Reviews number (MathSciNet)
MR2536702

Zentralblatt MATH identifier
1190.03051

#### Citation

Švejdar, Vítězslav. On Interpretability in the Theory of Concatenation. Notre Dame J. Formal Logic 50 (2009), no. 1, 87--95. doi:10.1215/00294527-2008-029. https://projecteuclid.org/euclid.ndjfl/1232375164

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