Notre Dame Journal of Formal Logic

Broadening the Iterative Conception of Set

Mark F. Sharlow

Abstract

The iterative conception of set commonly is regarded as supporting the axioms of Zermelo-Fraenkel set theory (ZF). This paper presents a modified version of the iterative conception of set and explores the consequences of that modified version for set theory. The modified conception maintains most of the features of the iterative conception of set, but allows for some non-wellfounded sets. It is suggested that this modified iterative conception of set supports the axioms of Quine's set theory NF.

Article information

Source
Notre Dame J. Formal Logic Volume 42, Number 3 (2001), 149-170.

Dates
First available in Project Euclid: 12 September 2003

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1063372198

Digital Object Identifier
doi:10.1305/ndjfl/1063372198

Mathematical Reviews number (MathSciNet)
MR2010179

Zentralblatt MATH identifier
1034.03052

Subjects
Primary: 00A30: Philosophy of mathematics [See also 03A05]
Secondary: 03E70: Nonclassical and second-order set theories

Keywords
iterative conception of set non-wellfounded sets NF

Citation

Sharlow, Mark F. Broadening the Iterative Conception of Set. Notre Dame J. Formal Logic 42 (2001), no. 3, 149--170. doi:10.1305/ndjfl/1063372198. http://projecteuclid.org/euclid.ndjfl/1063372198.


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References

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