In the present section we shall discuss the various systems of set theory which admit, beside sets, also **classes**. **Classes** are like sets, except that they can be very comprehensive; an extreme example of a **class** is the **class** which contains all sets. […] The main point which will, in our opinion, emerge from this analysis is that set theory with **classes** and set theory with sets only are not two separate theories; they are, essentially, different formulations of the same underlying theory.

1973, Abraham Fraenkel, Yehoshua Bar-Hillel, Azriel Lévy, Foundations of Set Theory, 2nd edition, Elsevier, page 119