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  1. Undecidability without Arithmetization.Andrzej Grzegorczyk - 2005 - Studia Logica 79 (2):163-230.
    In the present paper the well-known Gödels – Churchs argument concerning the undecidability of logic (of the first order functional calculus) is exhibited in a way which seems to be philosophically interestingfi The natural numbers are not used. (Neither Chinese Theorem nor other specifically mathematical tricks are applied.) Only elementary logic and very simple set-theoretical constructions are put into the proof. Instead of the arithmetization I use the theory of concatenation (formalized by Alfred Tarski). This theory proves to be an (...)
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  • Growing Commas. A Study of Sequentiality and Concatenation.Albert Visser - 2009 - Notre Dame Journal of Formal Logic 50 (1):61-85.
    In his paper "Undecidability without arithmetization," Andrzej Grzegorczyk introduces a theory of concatenation $\mathsf{TC}$. We show that pairing is not definable in $\mathsf{TC}$. We determine a reasonable extension of $\mathsf{TC}$ that is sequential, that is, has a good sequence coding.
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  • Interpretations, according to Tarski.Harvey Friedman - unknown
    The notion of interpretation is absolutely fundamental to mathematical logic and the foundations of mathematics. It is also crucial for the foundations and philosophy of science - although here some crucial conditions generally need to be imposed; e.g., “the interpretation leaves the mathematical concepts unchanged”.
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  • On Interpretability in the Theory of Concatenation.Vítězslav Švejdar - 2009 - Notre Dame Journal of Formal Logic 50 (1):87-95.
    We prove that a variant of Robinson arithmetic $\mathsf{Q}$ with nontotal operations is interpretable in the theory of concatenation $\mathsf{TC}$ introduced by A. Grzegorczyk. Since $\mathsf{Q}$ is known to be interpretable in that nontotal variant, our result gives a positive answer to the problem whether $\mathsf{Q}$ is interpretable in $\mathsf{TC}$. An immediate consequence is essential undecidability of $\mathsf{TC}$.
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  • Variants of Robinson's essentially undecidable theoryR.James P. Jones & John C. Shepherdson - 1983 - Archive for Mathematical Logic 23 (1):61-64.
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  • Arithmetic on semigroups.Mihai Ganea - 2009 - Journal of Symbolic Logic 74 (1):265-278.
    Relations between some theories of semigroups (also known as theories of strings or theories of concatenation) and arithmetic are surveyed. In particular Robinson's arithmetic Q is shown to be mutually interpretable with TC, a weak theory of concatenation introduced by Grzegorczyk. Furthermore, TC is shown to be interpretable in the theory F studied by Tarski and Szmielewa, thus confirming their claim that F is essentially undecidable.
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  • On a Theorem of Cobham Concerning Undecidable Theories.Robert L. Vaught, Ernest Nagel, Patrick Suppes & Alfred Tarski - 1969 - Journal of Symbolic Logic 34 (1):126-127.
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  • (1 other version)Concatenation as a basis for arithmetic.W. V. Quine - 1946 - Journal of Symbolic Logic 11 (4):105-114.
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