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Spring 1999 Subsystems of Quine's ``New Foundations'' with Predicativity Restrictions
M. Randall Holmes
Notre Dame J. Formal Logic 40(2): 183-196 (Spring 1999). DOI: 10.1305/ndjfl/1038949535

Abstract

This paper presents an exposition of subsystems $\mathit{NFP}$ and $\mathit{NFI}$ of Quine's $\mathit{NF}$, originally defined and shown to be consistent by Crabbé, along with related systems $\mathit{TTP}$ and $\mathit{TTI}$ of type theory. A proof that $\mathit{TTP}$ (and so $\mathit{NFP}$) interpret the ramified theory of types is presented (this is a simplified exposition of a result of Crabbé). The new result that the consistency strength of $\mathit{NFI}$ is the same as that of $\mathit{PA}_2$ is demonstrated. It will also be shown that $\mathit{NFI}$ cannot be finitely axiomatized (as can $\mathit{NF}$ and $\mathit{NFP}$).

Citation

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M. Randall Holmes. "Subsystems of Quine's ``New Foundations'' with Predicativity Restrictions." Notre Dame J. Formal Logic 40 (2) 183 - 196, Spring 1999. https://doi.org/10.1305/ndjfl/1038949535

Information

Published: Spring 1999
First available in Project Euclid: 3 December 2002

zbMATH: 0993.03066
MathSciNet: MR1816887
Digital Object Identifier: 10.1305/ndjfl/1038949535

Subjects:
Primary: 03E70
Secondary: 03B15, 03F35

Rights: Copyright © 1999 University of Notre Dame

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Vol.40 • No. 2 • Spring 1999
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