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Small Veblen ordinal

There is no standard notation for ordinals beyond the Feferman–Schütte ordinal ${\displaystyle \Gamma _{0}}$. Most systems of notation use symbols such as ${\displaystyle \psi (\alpha )}$, ${\displaystyle \theta (\alpha )}$, ${\displaystyle \psi _{\alpha }(\beta )}$, some of which are modifications of the Veblen functions to produce countable ordinals even for uncountable arguments, and some of which are "collapsing functions".

The small Veblen ordinal ${\displaystyle \theta _{\Omega ^{\omega }}(0)}$or${\displaystyle \psi (\Omega ^{\Omega ^{\omega }})}$ is the limit of ordinals that can be described using a version of Veblen functions with finitely many arguments. It is the ordinal that measures the strength of Kruskal's theorem. It is also the ordinal type of a certain ordering of rooted trees (Jervell 2005).

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