User blog:Moooosey/Simple psi-- a fairly simple ocf

Simple psi is defined thusly (it is closely related to madore's psi, to the point that I copied the LaTeX from that page and slightly modified it):

\begin{eqnarray*} C_0(\alpha) &=& \{0, 1, \Omega\}\\ C_{n+1}(\alpha) &=& \{\gamma + \delta, \psi(\eta) | \gamma, \delta, \eta \in C_n (\alpha); \eta < \alpha\} \\ C(\alpha) &=& \bigcup_{n < \omega} C_n (\alpha) \\ \psi(\alpha) &=& \min\{\beta \in \Omega|\beta \notin C(\alpha)\} \\ \end{eqnarray*}

I have a few questions about it.

1. What is \psi(\Omega)?

2. What is the limit of Simple psi?