original_query: What is New Foundations (NF) and how does it relate to the theory of types of Principia Mathematica?
query: What is New Foundations (NF) and how does it relate to the theory of types of Principia Mathematica?
answer: New Foundations (NF) is an axiomatic set theory created by Willard Van Orman Quine as a simplified version of the theory of types from Principia Mathematica.  NF uses the same well-formed formulas as Russellian unramified typed set theory (TST), a streamlined version of the theory of types, but without the type annotations.  NF's axioms are essentially those of TST with type indices removed.