Class Set-Class

Subclass-Of: Class, Relation, Set
Has-Instance: Eo-Set
Instance-Of: Class, Relation, Set
Arity: 1
Set-Class is a meta-Class. Its instances are special kinds of classes, all of whose instances are themselves sets (not Classes) such that every member of such a set is specified to be a member of a certain Class.


Arity: 1

Equivalence Axioms for Set-Class:

(<=> (Set-Class ?X0)
     (Exists (?Thing)
             (And (Class ?Thing)
                  (Forall (?Things)
                          (<=> (Instance-Of ?Things ?X0)
                               (And (Set ?Things)
                                    (Forall (?X)
                                            (=> (Member ?X ?Things)
                                                (Instance-Of ?X

Equivalence Axioms mentioning Set-Class:

(<=> (Eo-Set ?X0)
     (Exists (?Sc) (And (Set-Class ?Sc) (Instance-Of ?X0 ?Sc))))