User blog comment:Wythagoras/Extension of the busy beaver function/@comment-1605058-20131104183340/@comment-10429372-20131105162828

I think you don't understand it. We run first the oracle tape TM. Suppose it has 2 states, a ruleset for it is:

0 _ O r 1 0 O O r 1 1 _ O l 0 1 O O r halt

Its output is O(1) O(2) O(2) O(1), the number between brackets is the oracle's level. So we have a TM that runs using 2 super-oracles and 2 normal oracles.

Then we can construct a ruleset based on the fact that we have 2 super-oracles and 2 normal oracles.

With more than one oracle tape, we have oracles diagonalizing over the oracle TMs. But that is no problem, since oracles on the tape works similiar to 1s on the tape. The only difference is the counter.