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 Veblen hierarchy as extended to arbitrary finite numbers of arguments. Using Weiermann's theta function, it can be expressed as \(\vartheta(\Omega^\omega)\).

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