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Absolute $L$-realizability and intuitionistic logic

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.

Key words: constructive semantics, realizability, absolute realizability, formal arithmetic, intuitionistic logic.

UDC: 510.25+510.64

Received: 20.06.2018

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2019, 74:2, 79–82

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