🚀 go-pugleaf

In article <1992Nov04.233228.16942@Cookie.secapl.com> frank@Cookie.secapl.com
 (Frank Adams) writes:

   >Proper classes arose because it is hard to talk about sets in general
   >without them.  I think it is safe to say that most mathematicians are a bit
   >uncomfortable dealing with proper classes, but their use is at least
   >demonstrably consistent (at least if the underlying set theory is
   >consistent).

  Adding to a set theory T predicative class existence axioms (i.e. axioms
asserting the existence of classes definable by a formula containing
no quantifiers over classes) yields a conservative extension of T, and
the classes in such a case can be regarded as just a convenient way of
referring to formulas. Adding impredicative class existence axioms
yields an essentially stronger theory.