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6
votes
Succinctly naming big numbers: ZFC versus Busy-Beaver
This isn't an answer, but it's too long for a comment.
I don't think the computable ordinals are well enough defined for the function $f(n)$ to work. Suppose you give me a system mapping {$0,1$}$^* $ …
4
votes
Succinctly naming big numbers: ZFC versus Busy-Beaver
I have another question which is too long to fit into a comment: how do you even know that $f(n)$ is increasing?
If you have two Turing Machines $M$ and $M'$ that realize the same ordinal $\alpha$, …