\(\psi(\psi_I(0))\) is a large countable ordinal. Michael Rathjen's ordinal collapsing function \(\psi\) is used here along with \(I\), the first inaccessible cardinal. \(\psi_I(0)\) is the omega fixed point. It is the proof-theoritic ordinal of \(\Pi_1^1- ext{TR}_0\), a susbystem of second-order arithmetic. As there is not currently a notation to define \(\psi(\psi_I(0))\) on the ordinal notations article, we define a simple notation to do this below: Let \(\Omega_0=1\), and if \(\alpha>0\), let \(\Omega_\alpha=\omega_\alpha\). \(C_0(\alpha,\beta) = \beta\) \(C(\alpha,\beta) = \bigcup_{n<\omega}C_n(\alpha,\beta)\)