User blog comment:Scorcher007/Large countable ordinal notation up to Z2 and ZFC/@comment-35470197-20181121071653/@comment-35470197-20181121141304

> But I still don't understand what the ambiguity of the concepts is.

If \(S[\sigma](\varepsilon_0)\) coincides with \(\varepsilon_0\)-th admissible as you wrote, then it should be recursibly inaccessible by definition.

Also, "1st fixed point of admissible" is what you really intend, right?