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- New_Foundations abstract "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. Quine first proposed NF in a 1937 article titled \"New Foundations for Mathematical Logic\"; hence the name. Much of this entry discusses NFU, an important variant of NF due to Jensen (1969) and exposited in Holmes (1998). In 1940 and 1951 Quine introduced an extension of NF sometimes called \"Mathematical Logic\" or \"ML\", that included classes as well as sets. New Foundations has a universal set, so it is a non well founded set theory. That is to say, it is a logical theory that allows infinite descending chains of membership such as…xn ∈ xn-1 ∈ …x3 ∈ x2 ∈ x1. It avoids Russell's paradox by only allowing stratifiable formulae in the axiom of comprehension. For instance x ∈ y is a stratifiable formula, but x ∈ x is not (for details of how this works see below).".
- New_Foundations wikiPageExternalLink s11225-008-9107-8.
- New_Foundations wikiPageExternalLink head.pdf.
- New_Foundations wikiPageExternalLink nf.html.
- New_Foundations wikiPageExternalLink setbiblio.html.
- New_Foundations wikiPageExternalLink ess.pdf.
- New_Foundations wikiPageExternalLink quine-nf.
- New_Foundations wikiPageExternalLink settheory-alternative.
- New_Foundations wikiPageID "945957".
- New_Foundations wikiPageLength "39660".
- New_Foundations wikiPageOutDegree "143".
- New_Foundations wikiPageRevisionID "701401172".
- New_Foundations wikiPageWikiLink Ali_Enayat.
- New_Foundations wikiPageWikiLink Alternative_set_theory.
- New_Foundations wikiPageWikiLink Atomic_formula.
- New_Foundations wikiPageWikiLink Automorphism.
- New_Foundations wikiPageWikiLink Axiom_of_choice.
- New_Foundations wikiPageWikiLink Axiom_of_extensionality.
- New_Foundations wikiPageWikiLink Axiom_of_reducibility.
- New_Foundations wikiPageWikiLink Axiom_schema_of_specification.
- New_Foundations wikiPageWikiLink Beth_number.
- New_Foundations wikiPageWikiLink Bijection.
- New_Foundations wikiPageWikiLink Binary_relation.
- New_Foundations wikiPageWikiLink Boolean_algebra_(structure).
- New_Foundations wikiPageWikiLink Burali-Forti_paradox.
- New_Foundations wikiPageWikiLink Cantors_paradox.
- New_Foundations wikiPageWikiLink Cantors_theorem.
- New_Foundations wikiPageWikiLink Cardinal_number.
- New_Foundations wikiPageWikiLink Cartesian_closed_category.
- New_Foundations wikiPageWikiLink Category:Systems_of_set_theory.
- New_Foundations wikiPageWikiLink Category:Type_theory.
- New_Foundations wikiPageWikiLink Category:Urelements.
- New_Foundations wikiPageWikiLink Category:Willard_Van_Orman_Quine.
- New_Foundations wikiPageWikiLink Circular_reasoning.
- New_Foundations wikiPageWikiLink Class_(set_theory).
- New_Foundations wikiPageWikiLink Complement_(set_theory).
- New_Foundations wikiPageWikiLink Consistency.
- New_Foundations wikiPageWikiLink Currying.
- New_Foundations wikiPageWikiLink Equiconsistency.
- New_Foundations wikiPageWikiLink Equinumerosity.
- New_Foundations wikiPageWikiLink Equivalence_class.
- New_Foundations wikiPageWikiLink Existential_quantification.
- New_Foundations wikiPageWikiLink Extensionality.
- New_Foundations wikiPageWikiLink Finitely_axiomatized.
- New_Foundations wikiPageWikiLink Function_(mathematics).
- New_Foundations wikiPageWikiLink Gottlob_Frege.
- New_Foundations wikiPageWikiLink Hierarchy.
- New_Foundations wikiPageWikiLink Implementation_of_mathematics_in_set_theory.
- New_Foundations wikiPageWikiLink Impredicativity.
- New_Foundations wikiPageWikiLink Injective_function.
- New_Foundations wikiPageWikiLink Kazimierz_Kuratowski.
- New_Foundations wikiPageWikiLink Large_cardinal.
- New_Foundations wikiPageWikiLink Mathematical_logic.
- New_Foundations wikiPageWikiLink Measurable_cardinal.
- New_Foundations wikiPageWikiLink Model_theory.
- New_Foundations wikiPageWikiLink Monotonic_function.
- New_Foundations wikiPageWikiLink Morse–Kelley_set_theory.
- New_Foundations wikiPageWikiLink Naive_set_theory.
- New_Foundations wikiPageWikiLink Norbert_Wiener.
- New_Foundations wikiPageWikiLink Ordered_pair.
- New_Foundations wikiPageWikiLink Ordinal_number.
- New_Foundations wikiPageWikiLink Paradox.
- New_Foundations wikiPageWikiLink Peano_axioms.
- New_Foundations wikiPageWikiLink Positive_set_theory.
- New_Foundations wikiPageWikiLink Power_set.
- New_Foundations wikiPageWikiLink Principia_Mathematica.
- New_Foundations wikiPageWikiLink Projection_(mathematics).
- New_Foundations wikiPageWikiLink Restriction_(mathematics).
- New_Foundations wikiPageWikiLink Robert_M._Solovay.
- New_Foundations wikiPageWikiLink Ronald_Jensen.
- New_Foundations wikiPageWikiLink Russells_paradox.
- New_Foundations wikiPageWikiLink Set-theoretic_definition_of_natural_numbers.
- New_Foundations wikiPageWikiLink Set_theory.
- New_Foundations wikiPageWikiLink Similarity_(geometry).
- New_Foundations wikiPageWikiLink Singleton_(mathematics).
- New_Foundations wikiPageWikiLink Stanford_Encyclopedia_of_Philosophy.
- New_Foundations wikiPageWikiLink Stratification_(mathematics).
- New_Foundations wikiPageWikiLink Theodore_Hailperin.
- New_Foundations wikiPageWikiLink Topos.
- New_Foundations wikiPageWikiLink Transfinite_induction.
- New_Foundations wikiPageWikiLink Truth_value.
- New_Foundations wikiPageWikiLink Type_theory.
- New_Foundations wikiPageWikiLink Ultrafilter.
- New_Foundations wikiPageWikiLink Universal_set.
- New_Foundations wikiPageWikiLink Urelement.
- New_Foundations wikiPageWikiLink Von_Neumann_universe.
- New_Foundations wikiPageWikiLink Von_Neumann–Bernays–Gödel_set_theory.
- New_Foundations wikiPageWikiLink Weakly_compact_cardinal.
- New_Foundations wikiPageWikiLink Well-formed_formula.
- New_Foundations wikiPageWikiLink Well-order.
- New_Foundations wikiPageWikiLink Willard_Van_Orman_Quine.
- New_Foundations wikiPageWikiLink Zermelo_set_theory.
- New_Foundations wikiPageWikiLink Zermelo–Fraenkel_set_theory.
- New_Foundations wikiPageWikiLinkText "ML".
- New_Foundations wikiPageWikiLinkText "Mathematical Logic".
- New_Foundations wikiPageWikiLinkText "NF".
- New_Foundations wikiPageWikiLinkText "NFU".
- New_Foundations wikiPageWikiLinkText "New Foundations".
- New_Foundations wikiPageWikiLinkText "different solution".
- New_Foundations authorlink "Hao Wang".