Permutations and wellfoundedness: the true meaning of the bizarre arithmetic of Quine's NF
Thomas Förster · Journal of Symbolic Logic · 2006
Abstract It is shown that, according to NF, many of the assertions of ordinal arithmetic involving theT-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 allurelemente.