Maybe you could put it in APL primitives, or SciSnap, but I want to experiment with ordinals and also make the Fast growing hierarchy with it. Also make a supremum / fixed point function in the library so that i can say things like e_0 = (fixed point (a) -> (w^a)). Also I don't know how to make scisnap sets and that type of stuff, and I failed on making another ordinal library.
Oh boy. Probably there is nobody here better qualified than you to design such a library. Perhaps you could find a collaborator to help with the coding and deployment.
Snap! Build Your Own Blocks (berkeley.edu)
I did it up until Omega+1 because it doesn't do it for FGH, although the rules of the ordinal are correct, do you have any idea on how to fix it?
$$\alpha+1= α \cup \begin{Bmatrix} \alpha\end{Bmatrix} $$, but FGH $$f_{\alpha+1}(n) = f^n_{\alpha}(n)$$There is a clear difference. Do you have any ideas to fix it without creating another block so that $$\omega+1 = \omega \cup \begin{Bmatrix}\omega\end{Bmatrix}$$ and $$f_{\omega+1}(n) = f_{\omega}^n(n)$$ without changing the block?
I'll have to look at this when it isn't 2am. :~/
I tried making another one but crashed before i could save (it still wasn't fixed), so i went back to the old one
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