On the consistency of an impredicative subsystem of Quine's NF

DOI10.2307/2273386zbMath0487.03024OpenAlexW2058981710WikidataQ56031501 ScholiaQ56031501MaRDI QIDQ3947653

Marcel Crabbé

Publication date: 1982

Published in: Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2273386

zbMATH Keywords

comprehension axiomNew Foundationspredicative logicfull second order logic

Mathematics Subject Classification ID

Cut-elimination and normal-form theorems (03F05) Consistency and independence results (03E35) Axiomatics of classical set theory and its fragments (03E30)

Related Items (8)

Increasing sentences in simple type theory ⋮ The equivalence of NF-style set theories with “tangled” type theories; the construction of ω-models of predicative NF (and more) ⋮ A fixed point theory over stratified truth ⋮ Symmetry as a criterion for comprehension motivating Quine's `New Foundations' ⋮ Term models for weak set theories with a universal set ⋮ Systems of combinatory logic related to predicative and ``mildly impredicative fragments of Quine's ``New Foundations ⋮ Subsystems of Quine's ``New Foundations with predicativity restrictions ⋮ Consistency of strictly impredicative NF and a little more …

Cites Work

• The consistency problem for NF
• A nonconstructive proof of Gentzen’s Hauptsatz for second order predicate logic
• The Axiom of Choice in Quine's New Foundations for Mathematical Logic
• Proof theory
• Unnamed Item

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