On interpretations of bounded arithmetic and bounded set theory

Details On interpretations of bounded arithmetic and bounded set theory On interpretations of bounded arithmetic and bounded set theory

2008-07-30

arxiv.org/abs/0807.4850v3

Mathematics

Logic

12 pages; section on omega-models removed due to error; references added and typos corrected

Scientific paper

In a recent paper, 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 ZF with the axiom of infinity negated are bi-interpretable: that is, they are mutually interpretable with interpretations that are inverse to each other. In this note, I describe a theory of sets that stands in the same relation to the bounded arithmetic IDelta0 + exp. Because of the weakness of this theory of sets, I cannot straightforwardly adapt Kaye and Wong's interpretation of arithmetic in set theory. Instead, I am forced to produce a different interpretation.

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