ИСТИНА

Сonstructive semantics based on the arithmetical computability are considered. The notion of arithmetical realizability for the language of formal arithmetic and its extensions is defined. In this framework, a notion of absolute arithmetical realizability for predicate formulas is introduced. It is proved that the semantics of arithmetical realizability for the language of formal arithmetic is the same as the standard classical semantics. The intuitionistic logic is not correct with respect to the semantics of absolute arithmetical realizability, but the basic logic is correct. It is proved that the semantics of absolute arithmetical realizability differs from the known constructive semantics based on primitive recursive computability.