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In mathematics and mathematical logic, a metatheory is a mathematical theory about another mathematical theory. (Source: Wikipedia)
4
votes
Enumerating all formulae of any first-order language
If you don't care about injectivity, you can use a Godel-numbering-like encoding, i.e.
$$
\mathtt{enum\_trm}(n) = \begin{cases}t &\text{if } n \text{ is } 2^\left<\text{index of constructor of }t\righ …