User blog comment:Edwin Shade/In Which I Try To Derive Values of Madore's OCF on My Own, and See How Far I Get/@comment-32213734-20171203100352/@comment-28606698-20171207175629

General set of rules for such kind of collapsing functions up to \(\Omega_{\omega}\)

Let \(\Omega_0=0\) and \(\Omega_{\nu+1}=\aleph_{\nu+1}\). Then:
 * 1) If \(\alpha=\psi_{\nu_1}(\beta_1)+\psi_{\nu_2}(\beta_2)+\cdots+\psi_{\nu_k}(\beta_k)\) then \(\text{cof}(\alpha)=\text{cof}(\psi_{\nu_k}(\beta_k))\) and \(\alpha[\eta]=\psi_{\nu_1}(\beta_1)+\cdots+\psi_{\nu_{k-1}}(\beta_{k-1})+\psi_{\nu_k}(\beta_k)[\eta]\),
 * 2) If \(\alpha=\psi_{\nu}(0)\), then \(\text{cof}(\alpha)=\omega\) and \(\alpha[0]=\Omega_{\nu}+1\) and \(\alpha[\eta+1]=\omega^{\alpha[\eta+1]}\),
 * 3) If \(\alpha=\psi_{\nu}(\beta+1)\) then \(\text{cof}(\alpha)=\omega\) and \(\alpha[0]=\psi_{\nu}(\beta)+1\) and \(\alpha[\eta+1]=\omega^{\alpha[\eta+1]}\),
 * 4) If \(\alpha=\Omega_{\nu+1}\) then \(\text{cof}(\alpha)=\Omega_{\nu+1}\) and \(\alpha[\eta]=\eta\)
 * 5) If \(\alpha=\psi_{\nu}(\beta)\) and \(\text{cof}(\beta)\in\{\omega\}\cup\{\Omega_{\mu+1}|\mu<\nu\}\) then \(\text{cof}(\alpha)=\text{cof}(\beta)\) and \(\alpha[\eta]=\psi_{\nu}(\beta[\eta])\),
 * 6) If \(\alpha=\psi_{\nu}(\beta)\) and \(\text{cof}(\beta)\in\{\Omega_{\mu+1}|\mu\geq\nu\}\) then \(\text{cof}(\alpha)=\omega\) and \(\alpha[\eta]=\psi_{\nu}(\beta[\gamma[\eta]])\) with \(\gamma[0]=\Omega_\mu\)  and \(\gamma[\eta+1]=\psi_\mu(\beta[\gamma[\eta]])\).