Notre Dame Journal of Formal Logic

On Interpretability in the Theory of Concatenation

Vítězslav Švejdar

Abstract

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

Permanent link to this document
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

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

Keywords
concatenation interpretability Robinson arithmetic essential undecidability

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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References

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