User blog comment:Fejfo/Uncountable indexed veblen function/@comment-32213734-20180513045616/@comment-30869823-20180514145037

I don't understand your proof of \( \Gamma_0\not=sup\{ β<\Gamma_0 : \varphi_\beta(\beta)\} \). You are right \( \Gamma_0\not=\varphi(\Gamma_0,\Gamma_0) \) but I still think \( \varphi_{\Omega+1} \) grows at about the same rate as \( \Gamma \)

EDIT: I found out \( \varphi_\Omega(\omega)[n]=\varphi_\omega(\omega)[n]=\varphi_n(\omega)\not=\varphi_n(n)=\varphi_\Omega(n) \) this is a counter example to continuity, you are right.

However I still think it would work using my weak fixed points (changing it right now)