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


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.