User blog comment:Deedlit11/Ordinal Notations VII: Indescribables/@comment-25337554-20171217095001/@comment-30754445-20171217104203

If I understand part VI correctly, then Ξ and K are already doing the kind of diagonalization your talking about. Roughly speaking:

Ξ(na gets you the Ωs

Ξ(K+a) gets you to the inacessible level.

Ξ(2K+a) gets you the Mahlos.

So no, you can't "diagonalize over all these steps" because the K/Ξ step is fundamentally different than all the previous ones. It's like asking if we can diagonalize over ε, ζ, η and Γ. Since the Γ function is already a diagonalization over the first the three functions, its a pretty meaningless question.

What you're really looking for here, is for a way to systematically repeat the K/Ξ step again and again. But given all the errors and ambiguities that crept into the previous levels (see the current discussing in the comments of part V), I would personally prefer that we'll double check and polish the previous levels until they are 100% right before we rush headlong towards new horizons.