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-32213734-20200220092514

So, for example, let we have collection of normal functions as a "collection of class-functions", and then we define a "second-order function", which input is a normal function, and output is function, enumerating its fixed points. As I understand, it is invalid in ZFC, and to work with such "second-order functions" we need an axiomatic system more powerful than ZFC? Or, maybe, one can prove using ZFC axioms that such "second-order functions" do not exist? (I guess the first option is correct, since to prove or disprove it one need to consider "a collection of classes", but it is invalid in ZFC).