Veblen function
The Veblen function is used to obtain larger ordinal numbers^{} than those provided by exponentiation^{}. It builds on a hierarchy of closed and unbounded^{} classes:

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$Cr(0)$ is the additively indecomposable numbers, $\mathbb{H}$

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$Cr(Sn)=Cr{(n)}^{\prime}$ the set of fixed points of the enumerating function of $Cr(n)$

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The Veblen function ${\phi}_{\alpha}\beta $ is defined by setting ${\phi}_{\alpha}$ equal to the enumerating function of $Cr(\alpha )$.
We call a number $\alpha $ strongly critical if $\alpha \in Cr(\alpha )$. The class of strongly critical ordinals is written $\mathrm{\mathbf{S}\mathbf{C}}$, and the enumerating function is written ${f}_{\mathrm{\mathbf{S}\mathbf{C}}}(\alpha )={\mathrm{\Gamma}}_{\alpha}$.
${\mathrm{\Gamma}}_{0}$, the first strongly critical ordinal, is also called the FefermanSchutte ordinal.
Title  Veblen function 

Canonical name  VeblenFunction 
Date of creation  20130322 13:29:10 
Last modified on  20130322 13:29:10 
Owner  Henry (455) 
Last modified by  Henry (455) 
Numerical id  4 
Author  Henry (455) 
Entry type  Definition 
Classification  msc 03E10 
Classification  msc 03F15 
Defines  strongly critical 
Defines  FefermanSchutte ordinal 