Hacker News Reader

Which one? I don't think so tbh because his proof uses PA.

The reason that [Gödel 1931] was influential was that it

claimed to prove incompleteness for a system for the

foundations of mathematics.

1st-order systems such a PA were introduced later and

quickly shown to be inadequate for the foundations of mathematics.

It's very easy for you to check this from his 1931 article.

If you figure this out correctly you can claim the third incompleteness theorem. (If I am right)

Results in [Gödel 1931] depend on existence of proposition

I'mUnprovable. Since, the proposition doesn't exist in

foundations, the results in [Gödel 1931] do not hold for foundations.

Yes, it is very easy to check that [Gödel 1931] was for a

system for the foundation of mathematics.