## Notre Dame Journal of Formal Logic

### Weak Theories of Concatenation and Arithmetic

Yoshihiro Horihata

#### Abstract

We define a new theory of concatenation WTC which is much weaker than Grzegorczyk's well-known theory TC. We prove that WTC is mutually interpretable with the weak theory of arithmetic R. The latter is, in a technical sense, much weaker than Robinson's arithmetic Q, but still essentially undecidable. Hence, as a corollary, WTC is also essentially undecidable.

#### Article information

Source
Notre Dame J. Formal Logic, Volume 53, Number 2 (2012), 203-222.

Dates
First available in Project Euclid: 9 May 2012

https://projecteuclid.org/euclid.ndjfl/1336588251

Digital Object Identifier
doi:10.1215/00294527-1715698

Mathematical Reviews number (MathSciNet)
MR2925278

Zentralblatt MATH identifier
1251.03075

Subjects
Primary: 03F25: Relative consistency and interpretations

#### Citation

Horihata, Yoshihiro. Weak Theories of Concatenation and Arithmetic. Notre Dame J. Formal Logic 53 (2012), no. 2, 203--222. doi:10.1215/00294527-1715698. https://projecteuclid.org/euclid.ndjfl/1336588251

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