Gödel-numbering (in its broadest meaning, not necessarily the one Gödel used): On one side, it would seem that an assignment of a symbol to a number is just a first order function, and the recursion set up to translate a formula into numbers would be first-order, but on the other hand the process is a function whose domain is the collection of all strings of symbols from the alphabet , which is a superset of the set of all formulas, and so that sounds second-order to me.(adsbygoogle = window.adsbygoogle || []).push({});

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# Is Gödel numbering a first or second order function?

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