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Intelligent systems. Theory and applications, 2019, Volume 23, Issue 2, Pages 159–163 (Mi ista234)  
Part 3. Mathematical models

The Zermelo–Fraenkel set theory is not sound with respect to the constructive sematics based on hyperarithmetic sorts

A. Yu. Konovalov
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Abstract: A semantics of the realizability based on hyperarithmetical sorts for formulas of the language of set theory is introduced. The soundness of axioms of the Zermelo–Fraenkel set theory with respect to this semantics is studied.
Keywords: constructive semantics, realizability, axiomatic set theory, hyperarithmetical sorts.
Document Type: Article
Language: Russian
Citation: A. Yu. Konovalov, “The Zermelo–Fraenkel set theory is not sound with respect to the constructive sematics based on hyperarithmetic sorts”, Intelligent systems. Theory and applications, 23:2 (2019), 159–163
Citation in format AMSBIB
\Bibitem{Kon19}
\by A.~Yu.~Konovalov
\paper The Zermelo--Fraenkel set theory is not sound with respect to the constructive sematics based on hyperarithmetic sorts
\jour Intelligent systems. Theory and applications
\yr 2019
\vol 23
\issue 2
\pages 159--163
\mathnet{http://mi.mathnet.ru/ista234}
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