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

Thomas Forster

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    5 Citations (Scopus)


    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.
    Original languageEnglish
    Pages (from-to)227-240
    Number of pages14
    JournalJournal of Symbolic Logic
    Issue number1
    Publication statusPublished - 2006

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