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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
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.
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- Copyright © Association for Symbolic Logic 2006
References
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