Feferman–Schütte ordinal

In mathematics, the Feferman–Schütte ordinal Γ₀ is a large countable ordinal. It is the proof-theoretic ordinal of several mathematical theories, such as arithmetical transfinite recursion. It is named after Solomon Feferman and Kurt Schütte, the former of whom suggested the name Γ₀.

There is no standard notation for ordinals beyond the Feferman–Schütte ordinal. There are several ways of representing the Feferman–Schütte ordinal, some of which use ordinal collapsing functions: ${\displaystyle \psi (\Omega ^{\Omega })}$, ${\displaystyle \theta (\Omega )}$, ${\displaystyle \varphi _{\Omega }(0)}$, or ${\displaystyle \varphi (1,0,0)}$.