Theorems of a foundational system are not computationally enumerable (in fact they are not even countable). See the following article: https://papers.ssrn.c

Theorems of a foundational system are not computationally enumerable (in fact they are not even countable). See the following article: https://papers.ssrn.com/abstract=3603021 https://papers.ssrn.com/abstract=3603021 In a foundational system, there are true propositions that cannot be proved. For example, is true but unprovable that an algorithm can enumerate the theorems of an order abstracted from strings.