Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 53, Number 2 (2012), 203-222.
Weak Theories of Concatenation and Arithmetic
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.
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
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