## Notre Dame Journal of Formal Logic

### Iteration One More Time

Roy T. Cook

#### Abstract

A neologicist set theory based on an abstraction principle (NewerV) codifying the iterative conception of set is investigated, and its strength is compared to Boolos's NewV. The new principle, unlike NewV, fails to imply the axiom of replacement, but does secure powerset. Like NewV, however, it also fails to entail the axiom of infinity. A set theory based on the conjunction of these two principles is then examined. It turns out that this set theory, supplemented by a principle stating that there are infinitely many nonsets, captures all (or enough) of standard second-order ZFC. Issues pertaining to the axiom of foundation are also investigated, and I conclude by arguing that this treatment provides the neologicist with the most viable reconstruction of set theory he is likely to obtain.

#### Article information

Source
Notre Dame J. Formal Logic Volume 44, Number 2 (2003), 63-92.

Dates
First available in Project Euclid: 21 April 2004

https://projecteuclid.org/euclid.ndjfl/1082637805

Digital Object Identifier
doi:10.1305/ndjfl/1082637805

Mathematical Reviews number (MathSciNet)
MR2060056

Zentralblatt MATH identifier
1071.03038

Subjects
Primary: 03E05: Other combinatorial set theory

#### Citation

Cook, Roy T. Iteration One More Time. Notre Dame J. Formal Logic 44 (2003), no. 2, 63--92. doi:10.1305/ndjfl/1082637805. https://projecteuclid.org/euclid.ndjfl/1082637805

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