User blog comment:Fejfo/Super Fast Beaver Hierarchies and a weird OCF/@comment-35470197-20180806040506/@comment-30869823-20180806072909

Yes I realized this too. \( \Omega \) as an order \( \Omega \) program doesn't work because this would mean it's index has to be larger than itself which is a contradiction so there is no program for \( \Omega \) so my notiation is constant for uncountable ordinals.

the definition of an order \( \alpha \) bitf*ck program in this blogpost is a pair \( (\alpha,\text{a finite sequence of instructions}) \). I don't know if I need to define it more formal than that.

I have thought about ways to fix this, I don't know if a more traditional encoding of ordinals as well orderings would help but an infinite time version of bitf*ck might.

And is my usage of \( \omega^{CK}_\alpha \) correct?