In many incompleteness proofs there is a claim that, given a Gödel numbering function that encodes sequences of symbols of a given formal system, there is a formula of that formal system that ...

In many incompleteness proofs there is a claim that, given a Gödel numbering function that encodes sequences of symbols of a given formal system, there is a formula of that formal system that corresponds to that Gödel numbering function such that the formula itself can refer unambiguously to formulas of that formal system. This paper proves that this cannot be the case.

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