proper class

Noun

 * 1)  A class which is not a set.
 * 2) * 2004, Hartry Field, The Consistency of the Naive Theory of Properties,, One Hundred Years of Russell's Paradox: Mathematics, Logic, Philosophy, Walter de Gruyter, page 308,
 * It is true that the absence of proper classes in ZF is sometimes awkward. It is also true that adding proper classes in the usual ways (either predicative classes as in Gödel—Bernays, or impredicative ones as in Morse-Kelley is conceptually unsettling: in each case (and especially in the more convenient Morse-Kelley case) they "look too much like just another level of sets", and the fact that there is no entity that captures the extension of predicates true of proper classes suggests the introduction of still further entities ("super-classes" that can have proper classes as members), and so on ad infinitum.
 * It is true that the absence of proper classes in ZF is sometimes awkward. It is also true that adding proper classes in the usual ways (either predicative classes as in Gödel—Bernays, or impredicative ones as in Morse-Kelley is conceptually unsettling: in each case (and especially in the more convenient Morse-Kelley case) they "look too much like just another level of sets", and the fact that there is no entity that captures the extension of predicates true of proper classes suggests the introduction of still further entities ("super-classes" that can have proper classes as members), and so on ad infinitum.

Translations

 * Italian: classe propria