Rathjen's OCFs: Michael Rathjen made a variety of ordinal collapsing functions for proof-theoretic purposes, these include:
Rathjen's \( \psi \) for an ordinal analysis of KPM.
Rathjen's \( \Psi \) for an ordinal analysis of KP with the \( \Pi_3 \)-reflection schema adjoined.
Rathjen's \( \Psi \) for an ordinal analysis of lightface (parameterless) \( \Pi^1_2 \)-comprehension, which is equivalent to KP plus the assertion that there exists a stable ordinal.