Notre Dame Journal of Formal Logic

Weak Theories of Concatenation and Arithmetic

Yoshihiro Horihata


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

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

First available in Project Euclid: 9 May 2012

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Primary: 03F25: Relative consistency and interpretations

theory of concatenation Robinson's arithmetic interpretation


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

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