[ProfHewitt]

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

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.

[shikoba]

>there are true propositions that cannot be proved

In that case, they're not theorems. Theorem are things that can be proved starting from axioms. And proofs are enumerable, except if the axioms are not enumerable.