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THE POTENTIAL HIERARCHY OF SETS

Published online by Cambridge University Press:  14 March 2013

ØYSTEIN LINNEBO
ØYSTEIN LINNEBO*
Affiliation:
Birkbeck University of London and University of Oslo
*
*DEPARTMENT OF PHILOSOPHY, BIRKBECK UNIVERSITY OF LONDON, MALET STREET, LONDON WC1 7HX, UK
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Abstract

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.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 6 , Issue 2 , June 2013 , pp. 205 - 228
Copyright
Copyright © Association for Symbolic Logic 2013 

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