User blog comment:MilkyWay90/Finishing my very first notation - The Generalized Factorial/@comment-35470197-20190710234255/@comment-35470197-20190723021910

It depends on what "understandable" means. We do not have a well-defined sufficiently simple notation beyond the large cardinal level, therefore we do not have an appropriate way to analyse a notation beyond that level. As a result, any notation beyond that is automatically "inunderstandable". To be fair, there are many notations which covers \(\psi_0(\Omega_{\Omega_{\cdot_{\cdot_{\cdoot}}}})\), and my first notation is actually analysed by another googologist up to the level.

One of my aims to create the first notation is to give a new notation which can be used in analysis beyond the wealy hyper-inaccessible cardinal level. I am certain it is much simpler than Rathjen's original notation system, although it might be strictly weaker than it.