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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


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.


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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.


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

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

Primary: 03C62

Keywords: finite set theory , I Delta 0 + exp , interpretations

Rights: Copyright © 2009 University of Notre Dame


Vol.50 • No. 2 • 2009
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