Notre Dame Journal of Formal Logic

Broadening the Iterative Conception of Set

Mark F. Sharlow


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

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

First available in Project Euclid: 12 September 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

iterative conception of set non-wellfounded sets NF


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.

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