User:Wythagoras/Ordinals/Extension of the compact ordinal notation

This is the definition for the ordinals I've used in my blog post.

\(\psi_{\Xi(_20)}(0)\) is the first limit of \(\psi_{\Xi(K)}(0)\), \(\psi_{\Xi(K_K)}(0)\), \(\psi_{\Xi(K_{K_K})}(0)\), ...

\(\psi_{\Xi(_20)}(1)\) is the second limit of \(\psi_{\Xi(K)}(0)\), \(\psi_{\Xi(K_K)}(0)\), \(\psi_{\Xi(K_{K_K})}(0)\), ...

etc.

\(\psi_{\Xi(_21)}(0)\) is the limit of \(\psi_{\Xi(_20)}(\Xi(_20))\), \(\psi_{\Xi(_20)}(\Xi(_20)_{\Xi(_20)})\), ...

\(\psi_{\Xi(_22)}(0)\) is the limit of \(\psi_{\Xi(_21)}(\Xi(_21))\), \(\psi_{\Xi(_21)}(\Xi(_21)_{\Xi(_21)})\), ...

\(\psi_{\Xi(_2K)}(0)\) is the limit of \(\psi_{\Xi(_20)}(0)\), \(\psi_{\Xi(_2\psi_{\Xi(_20)}(0))}(0)\), ...

\(\psi_{\Xi(_30)}(0)\) is the limit of \(\psi_{\Xi(_2K)}(0)\), \(\psi_{\Xi(_2K_K)}(0)\), \(\psi_{\Xi(_2K_{K_K})}(0)\), ...

\(\psi_{\Xi(_\Omega0)}(0)\) is the limit of \(\psi_{\Xi(_10)}(0)\), \(\psi_{\Xi(_{\psi_{\Xi(_10)}(0)}0)}(0)\), ...

\(\psi_{(I)\Xi(_00)}(0)\) is the limit of \(\psi_{\Xi(_{\Omega}0)}(0)\), \(\psi_{\Xi(_{\Omega_\Omega}(0)\), ...

\(\psi_{\Xi(_{0,1}0)}(0)\) is the first fixed point of \(\psi_{(\alpha)\Xi(_{0}0)}(0) = \psi_{(\psi_{(\alpha)\Xi(_{0}0)}(0))\Xi(_{}0)}(0)\)