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New Foundations is the axiomatic set theory in Quine's 1937 article "New Foundations for Mathematical Logic"; it simplifies the theory of types of Principia Mathematica.
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New foundation in homotopy type theory
Is there any model of NF (New Foundations) on HoTT (homotopy type theory)?
Because there is a model of ZF(C) on HoTT (The HoTT book, Section 10.5) and NF on ZFC (by this Wikipedia articile), I think …