User blog comment:Rgetar/Designation for the next element of a class above an ordinal and some rules for booster-base/@comment-35470197-20200219005322/@comment-35470197-20200219131058

> When we write "let a = ...", then it is obvious that a depends on all things on the right side of this equation

It is only the case where the left hand side is actually a single letter. If it looks like a complicated symbol like Ω_x or f_ζ(ξ)^κ, then it is not obvious.

> so it can be considered as second-order function depending on both first-order function Ω• and α.

It is wrong. It is irrelevant to second orderness in formal logic. Every function is a first order object or a class, and every function which assigns a function to a given function is a first order object or a class by definition, because it is a function. If you meant that it assgns a function to a class, it is just ill-defined in ZFC set theory or its extensions with large cardinal axioms.