User blog comment:Syst3ms/A sketch for an — actually — formal definition of UNOCF/@comment-35470197-20180803231131/@comment-35470197-20180804111433

1) > But a rule doesn't apply if the previous one already did.

I see. So for 2), for example, if \(\kappa = \Omega_2\), then in order to compute \(\psi_{\kappa}(0)\), you apply \begin{eqnarray*} \psi_{\kappa}(0) = \psi_{C(1)}(0) = C(0) \end{eqnarray*} but not \begin{eqnarray*} \psi_{\kappa}(0) = \min \{\beta \mid \sup(D(\beta,0) \cap \kappa ) = \beta \wedge \beta \in D[\kappa]\}, \end{eqnarray*} right?

4) > The C function is more or less just placeholders for ordinals that collapse into smaller stuff, so, past I, the actual values of the C function don't matter, only how they collapse does, if that make any sense.

But the definition of \(D_{n+1}(\beta,\alpha)\) heavily deoends on the values of \(C\), because you used the \(<\) relation between \(C(\nu_{n-1},\ldots,\nu_0) \in D_n(\beta,\alpha)\) and \(\alpha\).

3) 6) > ask Nish

Ok.

@Alemagno12

Would you tell me the answers?