anyway

So here's my current understanding of the fast-growing hierarchy.

The successor function on an ordinal x corresponds to iterating its corresponding function x times, where x is the argument

Adding ω to that ordinal corresponds to getting the xth succeeding function, where x is the argument

And then multiplying ω corresponds to getting the function for that ordinal + ω*x, where x is the argument

Is this good so far?

So does diagonalizing in the same way get me exponentation, then the epsilon function, then the zeta function, and so on?