User blog comment:Fejfo/Uncountable indexed veblen function/@comment-24061664-20180515100323

Actually in the normal Veblen function

\(\varphi_\Gamma_\alpha(0)(0) = \Gamma_\alpha(0)\)

If you put \(\alpha = \Omega\), \(\varphi_\Omega(0) = \Omega\), which is quite obvious.

In this respect, following descrition of Ordinal notation is wrong.

\(\varphi_\Omega(0) = \theta_\Omega(0) = \Gamma_0\)

Actually

\(\theta_{\Gamma_1}(0) = \Gamma_0\) and \(\varphi_{\Gamma_1}(0) = \Gamma_1\), and the description that "for countable arguments, \(\theta_\alpha(\beta) = \varphi_\alpha(\beta)\). For this reason" is wrong. It should be changed to "for \(\alpha \le \Gamma_0\), \(\theta_\alpha(\beta) = \varphi_\alpha(\beta)\). For this reason"

I wrote it in the talk page in detail but no one has answered yet.