User blog comment:MilkyWay90/Help with understanding Veblen array notation/@comment-30754445-20180811202716/@comment-35392788-20180819122235

For the record, the only difference between UNOCF, and, say, Madore's psi is that UNOCF enumerates ordinals closed under addition while Madore's psi enumerates ordinals closed under exponentiation. And both actually work the same in all other regards. \(\Omega\) is also a wildcard in UNOCF. \(\psi(\alpha)\) is \(\omega^\alpha\), and once we get stuck, we use \(\Omega\) to get \(\psi(\Omega) = \varepsilon_0\). Not sure what was your point.