Permutations and Wellfoundedness: The True Meaning of the Bizarre Arithmetic of Quine's NF

Journal of Symbolic Logic 71 (1):227 - 240 (2006)

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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
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DOI 10.2178/jsl/1140641171
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Automorphisms of Models of Set Theory and Extensions of NFU.Zachiri McKenzie - 2015 - Annals of Pure and Applied Logic 166 (5):601-638.
On Hereditarily Small Sets in ZF.M. Randall Holmes - 2014 - Mathematical Logic Quarterly 60 (3):228-229.

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