User:Vel!/Extended Veblen function

We have the extended Veblen function \(\varphi(\alpha_0, \alpha_1, \alpha_2, \ldots)\):


 * \(\varphi(\alpha) = \omega^\alpha\) (or some other normal function of \(\alpha\), but the exponential map is the Veblen hierarchy)
 * \(\varphi(\alpha_0, \alpha_1, \alpha_2, \ldots, \alpha_{n - 1}, 0) = \varphi(\alpha_0, \alpha_1, \alpha_2, \ldots, \alpha_{n - 1})\)
 * \(\gamma \mapsto \varphi(\gamma, 0, \ldots, 0, \alpha_1, \alpha_2, \alpha_3, \ldots, \alpha_{n - 1})\) enumerates the fixed points of \(\xi \mapsto \varphi(0, \ldots, 0, \xi, \beta, \alpha_2, \alpha_3, \ldots, \alpha_{n - 1})\)