The strength of extensionality. I: Weak weak set theories with infinity

DOI10.1016/J.APAL.2008.09.010zbMath1166.03033OpenAlexW1996243733MaRDI QIDQ1006617

Kentaro Sato

Publication date: 25 March 2009

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apal.2008.09.010

zbMATH Keywords

proof-theoretic ordinalaxiom of regularityaxiom of extensionalityintensional set theoryproof-theoretic strength of the axioms of set theory

Mathematics Subject Classification ID

Foundations of classical theories (including reverse mathematics) (03B30) Nonclassical and second-order set theories (03E70) Second- and higher-order arithmetic and fragments (03F35) Relative consistency and interpretations (03F25)

Related Items (4)

A MARRIAGE OF BROUWER’S INTUITIONISM AND HILBERT’S FINITISM I: ARITHMETIC ⋮ The strength of extensionality. II: Weak weak set theories without infinity ⋮ A new model construction by making a detour via intuitionistic theories. I: Operational set theory without choice is \(\Pi_1\)-equivalent to KP ⋮ Full and hat inductive definitions are equivalent in NBG

Cites Work

• Set theory. An introduction to independence proofs. 2nd print
• Proof-theoretic analysis by iterated reflection
• On Evans's vague object from set theoretic viewpoint
• Kripke-Platek Set Theory and the Anti-Foundation Axiom
• The consistency of classical set theory relative to a set theory with intu1tionistic logic
• Forcing under Anti‐Foundation Axiom: An expression of the stalks
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