A class is a generalized set invented to get around Russell's antinomy while retaining the arbitrary criteria for membership which leads to difficulty for sets. The members of classes are sets, but it is possible to have the class C of "all sets which are not members of themselves" without producing a paradox (since C is a proper class (and not a set), it is not a candidate for membership in C). The distinction between classes and sets is a concept from von Neumann-Bernays-Gödel set theory.

aggregate | proper class | Russell's antinomy | set | type | von Neumann-Bernays-Gödel set theory