scientific article; zbMATH DE number 1450821

zbMath0959.03001MaRDI QIDQ4956001

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Publication date: 23 May 2000

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zbMATH Keywords

consistencyfinite axiomatizationNFUaxiom of choiceNew Foundationssurreal numbersNF with urelementsaxiom of small ordinalselementary topology of the real numbersrelative consistency strengthstratified \(\lambda\)-calculus

Mathematics Subject Classification ID

Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematical logic and foundations (03-01) Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations (03-02) Consistency and independence results (03E35) Nonclassical and second-order set theories (03E70)

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Canonical form of Tarski sets in Zermelo-Fraenkel set theory ⋮ On the strength of a weak variant of the axiom of counting ⋮ Foundations of applied mathematics. I ⋮ The Cardinal Squaring Principle and an Alternative Axiomatization of NFU ⋮ Approximating Cartesian closed categories in NF-style set theories ⋮ The axiom scheme of acyclic comprehension ⋮ Sets and plural comprehension ⋮ Characterization of model Mirimanov-von Neumann cumulative sets ⋮ Strong axioms of infinity in NFU ⋮ The usual model construction for NFU preserves information ⋮ Automorphisms of models of set theory and extensions of NFU ⋮ The 3-stratifiable theorems of \(\text{NFU}_\infty\) ⋮ Subsystems of Quine's ``New Foundations with predicativity restrictions ⋮ A single-sorted theory of multisets ⋮ Feferman’s Forays into the Foundations of Category Theory ⋮ Why is the universe of sets not a set? ⋮ ALGEBRAIC NEW FOUNDATIONS ⋮ A modern rigorous approach to stratification in NF/NFU

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