User blog comment:ArtismScrub/Hierarchical Cardinal Notation (HCN)/@comment-30118230-20180226215304

Well this isn't well defined beyond Ф(I,0) since you didn't show how to actually work with the notation beyond that,but from what I can see,if you continue in a similar fashion to Ф_{1,2,3,...} then the elast fixed point of Ф_a(0,1) should be $$\Xi(K,0)$$ since what you are doing is pretty much the alpha-Mahlo hierarchy.