### Weak Theories of Concatenation and Arithmetic

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

#### 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.

First Page:
Primary Subjects: 03F25
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Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1336588251
Digital Object Identifier: doi:10.1215/00294527-1715698
Mathematical Reviews number (MathSciNet): MR2925278
Zentralblatt MATH identifier: 06054426

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