 thus the order-type of the ordinals below \(\Omega_n\) which belong to the “Skolem hull” \(C^{{\Omega_{\omega}}}(\alpha,\rho)\) is \(\rho\). In more pictorial terms, \(\rho\) is said to be the \(\alpha^{th}\) collapse of \(\Omega_n\) since the order-type of \(\Omega_n\) viewed from within the structure \(C^{{\Omega_{\omega}}}(\alpha,\rho)\) is actually \(\rho\).