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-35470197-20200219222415

In the comment above, I referred to two possibilities of the meaning of the terminology of "second order". The first one is the second orderness in a formal logic, and does not fit in this case by the reason which I explained above. The second one is what you referred to now. As I wrote, if you want to regard it as a second order function which assigns a function to a class-function, you need to consider "a collection of class", which is invalid in ZFC set theory or its variant. Sorry for my explanation being unclear.