Back New Foundations German Nuevos Fundamentos Spanish New Foundations French New Foundations Hungarian Nuova fondazione Italian 新基礎集合論 Japanese 새 기초 Korean New Foundations Dutch 新基础集合论 Chinese
In mathematical logic, New Foundations (NF) is an axiomatic set theory, conceived by Willard Van Orman Quine as a simplification of the theory of types of Principia Mathematica.
New Foundations has a universal set, so it is a non-well-founded set theory.[1] That is to say, it is an axiomatic set theory that allows infinite descending chains of membership, such as ... xn ∈ xn-1 ∈ ... ∈ x2 ∈ x1. It avoids Russell's paradox by permitting only stratifiable formulas to be defined using the axiom schema of comprehension. For instance, x ∈ y is a stratifiable formula, but x ∈ x is not.