User blog comment:P進大好きbot/New Googological Ruler/@comment-36984051-20190614130500/@comment-35470197-20190614140136

Good. One of the aims of this ruler is to set levels so that every level naturally appears in googology. For example, there are many significant ordinals between \(\varepsilon_0\) and \(\Gamma_0\), but I think that notations much stronger than \(\epsilon_0\) usually goes beyond \(\Gamma_0\). That is why I only set \(\varphi(\omega,0)\) between them. Then beginners can easily understand what to learn next by referring to the next level.

Another aim is to create a completely well-defined ruler. For example, strictly speaking, UNOCF and stage cardinals are ill-defined although they are often used in analysis. DAN and BMS have never been proved to terminate although they are often used to express the strength of notations. Therefore I did not use them in my ruler.