Notre Dame Journal of Formal Logic 50 (2):141-152 (2009)

Authors
Richard Pettigrew
Bristol University
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 1 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 IDelta0 + 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.
Keywords interpretations  bounded arithmetic  weak set theory
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DOI 10.1215/00294527-2009-003
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References found in this work BETA

Existence and Feasibility in Arithmetic.Rohit Parikh - 1971 - Journal of Symbolic Logic 36 (3):494-508.
On Interpretations of Arithmetic and Set Theory.Richard Kaye & Tin Lok Wong - 2007 - Notre Dame Journal of Formal Logic 48 (4):497-510.
Die Widerspruchsfreiheit der Allgemeinen Mengenlehre.Wilhelm Ackerman - 1937 - Journal of Symbolic Logic 2 (4):167-167.

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