# Small Veblen ordinal

The small Veblen ordinal $\phi_{{\Omega^\omega}}(0)$ or $\theta(\Omega^\omega)$ or $\psi(\Omega^{\Omega^\omega})$ 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).