Notre Dame Journal of Formal Logic

On Interpretability in the Theory of Concatenation

Vítězslav Švejdar


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 $\mathsf{TC}$.

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

First available in Project Euclid: 19 January 2009

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Zentralblatt MATH identifier

Primary: 03B25: Decidability of theories and sets of sentences [See also 11U05, 12L05, 20F10] 03F25: Relative consistency and interpretations

concatenation interpretability Robinson arithmetic essential undecidability


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.

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