Journal
NOTRE DAME JOURNAL OF FORMAL LOGIC
Volume 53, Issue 2, Pages 203-222Publisher
DUKE UNIV PRESS
DOI: 10.1215/00294527-1715698
Keywords
theory of concatenation; Robinson's arithmetic; interpretation
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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.
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