User blog comment:Simply Beautiful Art/Intuition behind the Mahlo OCF/@comment-35470197-20190829142904/@comment-31663462-20190829155747

Just because Rathjen's chi works differently does not make it stronger.

And I'm not sure where you see any thetas here. At the end of this blog post, I explained how one could deduce things such as \(\psi_{\chi(M^M)}(0)=\sup\{0,\chi(M^0),\chi(M^{\chi(M^0)}),\dots\}\) vs \(\psi_{\chi(M^M+1)}(0)=\sup\{\chi(M^M),\chi(M^M)^{\chi(M^M)},\chi(M^M)^{\chi(M^M)^{\chi(M^M)}},\dots\}\).