---
tag: MBXHFT41PJ
kind: concept
name: Rathjen's psi function
sources:
  - wikipedia: en:68756880@r1361080235
    locator: Rathjen's psi function
    note: adopted
    mention: wikipedia://en/68756880
    sections: [Summary]
same_as:
  wikidata: Q108782366
  wikipedia: Rathjen's psi function
inventory: [8JS3F4979V]
---

## Summary

In mathematics, **Rathjen's $\psi$ psi function** is an ordinal collapsing function developed by Michael Rathjen. It collapses weakly Mahlo cardinals $M$ to generate large countable ordinals. A weakly Mahlo cardinal is a cardinal such that the set of regular cardinals below $M$ is closed under $M$ (i.e. all normal functions closed in $M$ are closed under some regular ordinal $< M$). Rathjen uses this to diagonalise over the weakly inaccessible hierarchy.