Veblen function

Summary

The Veblen functions $\varphi_\gamma$ are a hierarchy of normal functions on the ordinals, each one listing the fixed points of the ones before. They start from $\varphi_0(\alpha) = \omega^\alpha$, and they give names to large countable ordinals such as the epsilon numbers and the Feferman–Schütte ordinal $\Gamma_0$. The precise definition is by transfinite recursion on the index $\gamma$. They are a basic tool of ordinal notations and of ordinal analysis in proof theory.