Note: The first several parts may be the same as existing one. But just hold on, it will soon get crazy.

Up to Omega


I use ρ(Greek letter rho) for my OCF.

(x and y are ordinals)

C_0(\alpha)=\{0, x : x\leq \rho (\beta) \;\; (\beta < \alpha) \}

C_n(\alpha)=\{ x+y, xy : x,y \in C_{n-1}(\alpha) \}

C(\alpha)=\bigcup_{n<\omega} C_n(\alpha)

\rho(\alpha)=min \{ \gamma| \gamma \notin C(\alpha) \}

I don't know if it works, but I mean that one step in rho is "the smallest number that can't be acieved by addition and multiplication from current step."


\rho(0)=1, because the first step is zero and you can't get one from zero.







\rho(\omega 2)=\omega^{\omega^{\omega 2}}



The limit is \epsilon_0.

Stil calm

\Omega means a fixed point and keep going on.




\rho(\Omega 2)=\epsilon_1

\rho(\Omega 3)=\epsilon_2

\rho(\Omega \omega)=\epsilon_{\omega}



\rho(\Omega^2 2)=\zeta_1



\rho(\Omega^{\Omega 2})=\phi(2,0,0)


\rho(\Omega^{\Omega^{\Omega}})=SVO (Is it correct?)

Ad blocker interference detected!

Wikia is a free-to-use site that makes money from advertising. We have a modified experience for viewers using ad blockers

Wikia is not accessible if you’ve made further modifications. Remove the custom ad blocker rule(s) and the page will load as expected.