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-35470197-20180814081210

@Syst3ms

I see. So your analysis is valid for UNOCF but not for Buchholz's OCF, right? Then it is also helpful for me, beause I know few about the behaviour of UNOCF up to now.

One mystery is that not only you, but also Rpakr and Alemagno12 simultaneously misunderstood the behaviour of Buchholz's OCF in the completely same way. Do you know a reason...?

By the way, I would like to know more about UNOCF. If you have an answer to any one of the following, please tell me. Here I denote by \(U\) the UNOCF, and by \(\psi\) Buchholz' OCF.
 * 1) Do you have a presentation of \(\psi_0(\Omega_n)\) with \(0 < n < \omega\) by \(U\)'s? (For example, a formula like those which Ecl1psed278 told me above.)
 * 2) Do you have a presentation of \(\psi_{n_0}(\psi_{n_1}(\cdots \psi_{n_k}(0) \cdots))\) with \((n_0,n_1\ldots,n_k) \in \mathbb{N}^{k+1}\) by \(U\)'s?
 * 3) Do you have \(\psi_0(\Omega_{\infty}) = U(\Omega_{\infty})\)?
 * 4) Is the limit of pair sequence system believed to be \(U(\Omega_{\infty})\)?
 * 5) Does a pair sequence \((a_0,n_0)(a_1,n_1) \cdots (a_k,n_k)\) of standard form correspond to formal strings obtained by \(\psi_{n_0} \cdots \psi_{n_k}(0)\) ordered in this way with additional \(,+\) between them?

In particular, I am interested in 3 and 4. If you have 4 but not 3, then we do not know whether the limit of pair sequence system is \(\psi_0(\Omega_{\infty})\) or not. If you have 3 and 4, then I will be interested in how UNOCF goes beyond \(\psi_0(\psi_3(0))\), which is absolutely harder to go beyond than \(\psi_0(\psi_2(0))\).