List of functions

• Cantor normal form, or CNF
• The Veblen hierarchy
• Buchholz's psi
• Extended Buchholz's psi
• 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.
• Arai's OCFs^{(sort out)}
• Stegert's OCFs^{(sort out)}