User blog comment:Googleaarex/A new, really strong OCF definition?/@comment-5529393-20170731023317

Okay, a couple more questions:

When you write D[\alpha[\beta[D[\alpha[D_{\gamma+1}]]]]], are $$\alpha[D_{\gamma+1}],D[\alpha[D_{\gamma+1}]],\beta[D[\alpha[D_{\gamma+1}]]]$$, etc., all supposed to be different ordinals, or is the notation not meant to be broken up like that? If they do mean something, what is the definition of $$\alpha[D_{\gamma+1}]$$, or more generally, what is the definition of $$\alpha[\beta]$$ for general ordinals $$\alpha$$ and $$\beta$$?

I see your definition of $$\psi_{D[0]}(0)[n]$$; how is $$\psi_{D[0]}(1)[n]$$ defined?

What do you mean by $$\alpha$$ must be the subset of $$D[\beta]$$?