Small Veblen ordinal

Template:Short description In mathematics, the small Veblen ordinal is a certain large countable ordinal, named after Oswald Veblen. It is occasionally called the Ackermann ordinal, though the Ackermann ordinal described by Template:Harvtxt is somewhat smaller than the small Veblen ordinal.

There is no standard notation for ordinals beyond the Feferman–Schütte ordinal ${\mathrm{\Gamma }}_0$. Most systems of notation use symbols such as $\psi (\alpha )$, $\theta (\alpha )$, ${\psi }_{\alpha }(\beta )$, 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 ${\theta }_{{\mathrm{\Omega }}^{\omega }}(0)$ or $\psi ({\mathrm{\Omega }}^{{\mathrm{\Omega }}^{\omega }})$ 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 Template:Harv.

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