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Arithmetical realizability and basic logic

A. Yu. Konovalov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Absolute arithmetical realizability of predicate formulas is introduced. It is proved that the intuitionistic logic is not sound with this semantics, but the basic logic is sound.

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

UDC: 510.25; 510.64

Received: 08.12.2014

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2016, 71:1, 35–38

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