User blog comment:Kyodaisuu/Mashimo function/@comment-1605058-20140706065714/@comment-1605058-20140707064039

Iko, but with suffiscently convoluted set of rules for diagonalizers we can reach strength described by any countable ordinal. You need to specify how well behaved these rules are.

Kyodaisuu, but we have no evidence that halting oracle used by 2nd order Busy Beaver function is equivalent to CK ordinal. If you look at my recent forum post, I state the opposite.