Weak Theories of Concatenation and Arithmetic

Notre Dame Journal of Formal Logic 53 (2):203-222 (2012)
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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

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References found in this work

Concatenation as a basis for arithmetic.W. V. Quine - 1946 - Journal of Symbolic Logic 11 (4):105-114.
Undecidability without Arithmetization.Andrzej Grzegorczyk - 2005 - Studia Logica 79 (2):163-230.
Growing Commas. A Study of Sequentiality and Concatenation.Albert Visser - 2009 - Notre Dame Journal of Formal Logic 50 (1):61-85.
Arithmetic on semigroups.Mihai Ganea - 2009 - Journal of Symbolic Logic 74 (1):265-278.
On Interpretability in the Theory of Concatenation.Vítězslav Švejdar - 2009 - Notre Dame Journal of Formal Logic 50 (1):87-95.

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