Sets and classes as many

In this paper the view is developed that classes should not be understood a s individuals, but, rather, as 'classes as many' of individuals. To correla te classes with individuals 'labelling' and 'colabelling' functions are int roduced and sets identified with a certain subdomain of the classes on whic h the labelling and colabelling functions are mutually inverse. A minimal a xiomatization of the resulting system is formulated and some of its extensi ons are related to various systems of set theory, including nonwellfounded set theories.