The potential hierarchy of sets

Review of Symbolic Logic 6 (2):205-228 (2013)
Authors
Øystein Linnebo
University of Oslo
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.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1017/S1755020313000014
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 36,586
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Plural Quantification and Modality.Gabriel Uzquiano - 2011 - Proceedings of the Aristotelian Society 111 (2pt2):219-250.
E Pluribus Unum: Plural Logic and Set Theory.John P. Burgess - 2004 - Philosophia Mathematica 12 (3):193-221.
Bad Company Tamed.Øystein Linnebo - 2009 - Synthese 170 (3):371 - 391.
Modalising Plurals.Simon Hewitt - 2012 - Journal of Philosophical Logic 41 (5):853-875.
Idealist and Realist Elements in Cantor's Approach to Set Theory.I. Jane - 2010 - Philosophia Mathematica 18 (2):193-226.

Add more references

Citations of this work BETA

Against the Iterative Conception of Set.Edward Ferrier - forthcoming - Philosophical Studies:1-23.
Plurals and Modals.Øystein Linnebo - 2016 - Canadian Journal of Philosophy 46 (4-5):654-676.
Dummett on Indefinite Extensibility.Øystein Linnebo - 2018 - Philosophical Issues 28 (1):196-220.
Modal Structuralism and Reflection.Sam Roberts - forthcoming - Review of Symbolic Logic:1-38.

View all 16 citations / Add more citations

Similar books and articles

A Hierarchy of Hereditarily Finite Sets.Laurence Kirby - 2008 - Archive for Mathematical Logic 47 (2):143-157.
The Iterative Conception of Set.Thomas Forster - 2008 - Review of Symbolic Logic 1 (1):97-110.
The Hausdorff-Ershov Hierarchy in Euclidean Spaces.Armin Hemmerling - 2005 - Archive for Mathematical Logic 45 (3):323-350.
On Genericity and Ershov's Hierarchy.Amy Gale & Rod Downey - 2001 - Mathematical Logic Quarterly 47 (2):161-182.
Groundedness - Its Logic and Metaphysics.Jönne Kriener - 2014 - Dissertation, Birkbeck College, University of London
Two Simple Sets That Are Not Positively Borel.Wim Veldman - 2005 - Annals of Pure and Applied Logic 135 (1-3):151-209.
Sets Without Subsets of Higher Many-One Degree.Patrizio Cintioli - 2005 - Notre Dame Journal of Formal Logic 46 (2):207-216.
Wide Sets, ZFCU, and the Iterative Conception.Christopher Menzel - 2014 - Journal of Philosophy 111 (2):57-83.
Monotone Reducibility and the Family of Infinite Sets.Douglas Cenzer - 1984 - Journal of Symbolic Logic 49 (3):774-782.
Immunity and Hyperimmunity for Sets of Minimal Indices.Frank Stephan & Jason Teutsch - 2008 - Notre Dame Journal of Formal Logic 49 (2):107-125.

Analytics

Added to PP index
2015-02-06

Total downloads
162 ( #37,568 of 2,303,716 )

Recent downloads (6 months)
19 ( #25,154 of 2,303,716 )

How can I increase my downloads?

Monthly downloads

My notes

Sign in to use this feature