User blog comment:Googleaarex/Extended HyperNested Arrays/@comment-25418284-20130407213804/@comment-5529393-20130408031829

That's true. You can extend the various notations, but you have to be careful how you do it. For example, you can add the \(\varphi\) function to the closure functions, but that has some effect on the lower values, for example \(\psi(0)\) becomes \(\Gamma_0\). You can add higher cardinals - that may be the way to go here.