User blog comment:Googleaarex/Extended HyperNested Arrays/@comment-25418284-20130407213804/@comment-25418284-20130408050213

It looks like all ordinal collapsing functions stabilize (read: become constant) at some point. For Buchholz's psi function it's \(\Omega^{\Omega^{\Omega^{.^{.^.}}}} = \varepsilon_{\Omega + 1}\). From some values I've seen, it appears that \(\psi(\alpha) = \vartheta(\Omega^\alpha)\) holds for many values of \(\alpha\). Based on the scant information I have access to, I conclude that \(\vartheta(\varepsilon_{\Omega + 1}) = \psi(\varepsilon_{\Omega + 1}) = \text{BHO}\), which is the stabilization point of both psi and theta.

\(\psi\): Oppan Gangnam Style.