User blog comment:P進大好きbot/Please Help me on study of Pair Sequence System (2-rowed Bashicu Matrix System)/@comment-35870936-20180813215517/@comment-35392788-20180815124811

> I am a little confused about what \(\psi(\Omega_{\omega})\) appearing in the left hand side in the equality \(\psi(\Omega_{\omega}) = \psi(\psi_1(\psi_2(\cdots)))\) means. Is it Deedlit's \(\psi\)? Or is it Buchholz's \(\psi\)?

It is Deedlit's \(\psi\).

> I appreciate if you give me which definition of KOCF you are refering to, because Deedlit has constructed several OCFs.

I realized that what I was writing was in fact Deedlit's weakly Mahlo OCF, described here. His weakly compact OCF (described here) isn't notated like that, but, conveniently for us, \(\psi_\pi(\alpha)\) in his weakly Mahlo OCF is equal to \(\Psi_\pi(0,\alpha)\) in his weakly compact OCF. But the difference between the two doesn't matter right now, since they behave exactly the same way for our purposes.

> By the way, I noticed that UNOCF works in a similar way to Bashicu's OCF, which can be found here, in the analysis of pair sequence system. It is interesting.

Bashicu's OCF is actually a exponentiation-based OCF, and it's basically Madore's psi extended to higher cardinalities. But, again, the differences between addition-based (like UNOCF), exponentiation-based (like Bashicu's OCF) or Veblen-based (like Deedlit's OCF) OCFs fade away at such high levels.