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Sets and Classes as Many

John L. Bell
Journal of Philosophical Logic
Vol. 29, No. 6 (Dec., 2000), pp. 585-601
Published by: Springer
Stable URL: http://www.jstor.org/stable/30226709
Page Count: 17
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Sets and Classes as Many
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Abstract

In this paper the view is developed that classes should not be understood as individuals, but, rather, as "classes as many" of individuals. To correlate classes with individuals "labelling" and "colabelling" functions are introduced and sets identified with a certain subdomain of the classes on which the labelling and colabelling functions are mutually inverse. A minimal axiomatization of the resulting system is formulated and some of its extensions are related to various systems of set theory, including nonwellfounded set theories.

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