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2009 On Interpretations of Bounded Arithmetic and Bounded Set Theory
Richard Pettigrew
Notre Dame J. Formal Logic 50(2): 141-151 (2009). DOI: 10.1215/00294527-2009-003

Abstract

In "On interpretations of arithmetic and set theory," Kaye and Wong proved the following result, which they considered to belong to the folklore of mathematical logic.

Theorem The first-order theories of Peano arithmetic and Zermelo-Fraenkel set theory with the axiom of infinity negated are bi-interpretable.

In this note, I describe a theory of sets that is bi-interpretable with the theory of bounded arithmetic I Δ0 +exp . Because of the weakness of this theory of sets, I cannot straightforwardly adapt Kaye and Wong's interpretation of the arithmetic in the set theory. Instead, I am forced to produce a different interpretation.

Citation

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Richard Pettigrew. "On Interpretations of Bounded Arithmetic and Bounded Set Theory." Notre Dame J. Formal Logic 50 (2) 141 - 151, 2009. https://doi.org/10.1215/00294527-2009-003

Information

Published: 2009
First available in Project Euclid: 11 May 2009

zbMATH: 1183.03029
MathSciNet: MR2535581
Digital Object Identifier: 10.1215/00294527-2009-003

Subjects:
Primary: 03C62

Rights: Copyright © 2009 University of Notre Dame

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Vol.50 • No. 2 • 2009
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