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math.LO2008
On interpretations of bounded arithmetic and bounded set theory
Richard Pettigrew
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 arit…
math.LO2007
Natural Number Arithmetic in the Theory of Finite Sets
J. P. Mayberry, Richard Pettigrew
We describe a theory of finite sets, and investigate the analogue of Dedekind's theory of natural number systems (simply infinite systems) in this theory. Unlike the infinitary cas…