 To get a better feel for what \(\psi_{\sOmega_{n}}\) is doing, note that if \(\rho={\psi_{\sOmega_{n}}(\alpha)}\), then \(\rho&lt;\Omega_n\) and with \([\rho,\Omega_n)\) being the interval consisting of ordinals \(\rho\leq\alpha&lt;\Omega_n\) one has 