Sets and classes as many

Journal of Philosophical Logic 29 (6):585-601 (2000)
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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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John L. Bell
University of Western Ontario

Citations of this work

Varieties of Indefinite Extensibility.Gabriel Uzquiano - 2015 - Notre Dame Journal of Formal Logic 56 (1):147-166.
Russell's Paradox and the Theory of Classes in The Principles of Mathematics.Yasushi Nomura - 2013 - Journal of the Japan Association for Philosophy of Science 41 (1):23-36.

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References found in this work

Sets.Erik Stenius - 1974 - Synthese 27 (1-2):161 - 188.
Ackermann's set theory equals ZF.William N. Reinhardt - 1970 - Annals of Mathematical Logic 2 (2):189.

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