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Published online by Cambridge University Press:  14 March 2013

Birkbeck University of London and University of Oslo


Some reasons to regard the cumulative hierarchy of sets as potential rather than actual are discussed. Motivated by this, a modal set theory is developed which encapsulates this potentialist conception. The resulting theory is equi-interpretable with Zermelo Fraenkel set theory but sheds new light on the set-theoretic paradoxes and the foundations of set theory.

Research Article
Copyright © Association for Symbolic Logic 2013 

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