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The intuitionistic logic is not sound with $L$-realizability

A. Yu. Konovalov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: An absolute $L$-realizability of predicate formulas is introduced for all countable extensions $L$ of the language of arithmetic. It is proved that the intuitionistic logic is not sound with this semantics.

Keywords: constructive semantics, realizability, absolute realizability, formal arithmetic, intuitionistic logic.