Mathematica follows from the computational undecidability of
the Halting Problem.
Prior to https://papers.ssrn.com/abstract=3603021,
attempts to proof inferential incompleteness were
*incorrect* for foundational theories because of the
incorrect assumption that theorems of a foundational
theory can be computationally enumerated.
What is actually needed is a correct exposition (such as
https://papers.ssrn.com/abstract=3603021) of how
inferential incompleteness of Russell's Principia
Mathematica follows from the computational undecidability of
the Halting Problem.