Small Veblen ordinal

The small Veblen ordinal is the limit of the following sequence of ordinals \(\varphi(1, 0),\varphi(1, 0, 0),\varphi(1, 0, 0, 0),\varphi(1, 0, 0, 0, 0),\ldots\) where \(\varphi\) is the extended Veblen function. Using Weiermann's theta function, it can be expressed as \(\vartheta(\Omega^\omega)\).

Harvey Friedman's tree(n) function (for unlabeled trees) grows at around the same rate as \(f_{\vartheta(\Omega^\omega)}(n)\) in the fast-growing hierarchy.