 As an example we will introduce an ordinal representation system which characterizes the theory \((\Pi^1_1{\Hy}\bCA)+{{\BI}}\), following Buchholz 1977b. It is based on certain ordinal functions \(\psi_{\sOmega_n}\) which are often called collapsing functions. The definition of these functions, that is of the value \({\psi_{\sOmega_{n}}(\alpha)}\) at \(\alpha\), proceeds by recursion on \(\alpha\) and gets intertwined with the definition of sets of ordinals \(C^{{\Omega_{\omega}}}(\alpha,\beta)\), dubbed “Skolem hulls” since they are defined as the smallest structures closed under certain functions specified below.