Comment by Scarblac
8 months ago
And also, if BB were computable, then it could be used to solve the halting problem: run the Turing machine of size n for BB(n) steps, and if it hasn't halted yet, it never will. So the BB function is clearly not computable.
But to me as a layman that seems true regardless of formal axioms chosen, but I guess I need to read that linked thesis.
That is the standard argument for why BB is uncomputable for general n, but it's not the same as why BB(n) would be independent of ZFC for fixed n.