The strength of extensionality. II: Weak weak set theories without infinity

DOI10.1016/j.apal.2010.11.001zbMath1223.03044OpenAlexW2089061648MaRDI QIDQ639665

Kentaro Sato

Publication date: 22 September 2011

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.2010.11.001

zbMATH Keywords

bounded arithmeticprovably total functionsbounded reverse mathematicscomplexities below \(\mathbf P\)finite set theorygraphic conception of setssubtheories of \(\mathbf {V}^0\)weak set-theoretic axioms

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)

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Admissible closures of polynomial time computable arithmetic, Classes and truths in set theory, 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

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