 The theory of sets (classes) in PM is based on a number of contextual definitions, similar in some ways to the theory of descriptions. In what follows we will occasionally use the expression “class” for the PM notion, to remind the reader of the differences between this and an axiomatic theory of sets, such as ZF, not to indicate that these are “proper classes” in the sense used in ZF or VGB class theory, to indicate an expression that does not define a set, such as \(\{ x \mid x = x \}\), which is true of the universe \(\rV\) and so too “large” to be a set.