New V, ZF and abstractiont

Philosophia Mathematica 7 (3):293-321 (1999)

Authors
Stewart Shapiro
Ohio State University
Alan Weir
University of Glasgow
Abstract
We examine George Boolos's proposed abstraction principle for extensions based on the limitation-of-size conception, New V, from several perspectives. Crispin Wright once suggested that New V could serve as part of a neo-logicist development of real analysis. We show that it fails both of the conservativeness criteria for abstraction principles that Wright proposes. Thus, we support Boolos against Wright. We also show that, when combined with the axioms for Boolos's iterative notion of set, New V yields a system equivalent to full Zermelo-Fraenkel set theory with a principle of global choice. This advances Boolos's longstanding interest in the foundations of set theory.
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DOI 10.1093/philmat/7.3.293
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References found in this work BETA

Die Grundlagen der Arithmetik.Gottlob Frege - 1988 - Felix Meiner Verlag.
Frege’s Conception of Numbers as Objects.C. Wright - 1983 - Critical Philosophy 1 (1):97.
The Iterative Conception of Set.George Boolos - 1971 - Journal of Philosophy 68 (8):215-231.

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Citations of this work BETA

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Neo-Fregeanism and Quantifier Variance.Theodore Sider - 2007 - Aristotelian Society Supplementary Volume 81 (1):201–232.
Relative Categoricity and Abstraction Principles.Sean Walsh & Sean Ebels-Duggan - 2015 - Review of Symbolic Logic 8 (3):572-606.

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