## FANDOM

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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 $$\vartheta(\Omega^\omega)$$.

Using the Veblen hierarchy as extended to transfinitely many arguments, it is equal to $$\varphi_{\Omega^\omega}(0)$$

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.