Abstract
In the present paper the well-known Gödel’s – Church’s 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 appropriate tool. The decidability is defined directly as the property of graphical discernibility of formulas.
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Grzegorczyk, A. Undecidability without Arithmetization. Stud Logica 79, 163–230 (2005). https://doi.org/10.1007/s11225-005-2976-1
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DOI: https://doi.org/10.1007/s11225-005-2976-1