## FANDOM

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The Ackermann ordinal is equal to $$\varphi(1,0,0,0)$$ using phi function, $$\vartheta(\Omega^3)$$ using Weiermann's theta function, $$\theta(\Omega^2)$$ using Bird's theta function and $$\psi_0(\Omega^{\Omega^2})$$ using Buchholz's psi function (see ordinal notation).

It is first fixed point of map $$\alpha\rightarrow\varphi(\alpha,0,0)$$, and also smallest ordinal beyond reach of 3-argument Veblen function.