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Permutations and wellfoundedness: the true meaning of the bizarre arithmetic of Quine's NF

Published online by Cambridge University Press:  12 March 2014

Thomas Forster
Thomas Forster*
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, Cb3 0Wb, United Kingdom. E-mail: [email protected]
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Abstract

It is shown that, according to NF, many of the assertions of ordinal arithmetic involving the T-function which is peculiar to NF turn out to be equivalent to the truth-in-certain-permutation-models of assertions which have perfectly sensible ZF-style meanings, such as: the existence of wellfounded sets of great size or rank, or the nonexistence of small counterexamples to the wellfoundedness of ∈. Everything here holds also for NFU if the permutations are taken to fix all urelemente.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 71 , Issue 1 , March 2006 , pp. 227 - 240
Copyright
Copyright © Association for Symbolic Logic 2006

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References

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