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Modified realizability and predicate logic. (English. Russian original) Zbl 0912.03027
Math. Notes 61, No. 2, 212-220 (1997); translation from Mat. Zametki 61, No. 2, 259-269 (1997).
Summary: Semantics of predicate formulas based on the notion of modified realizability for arithmetic formulas and interpretations of the language of arithmetic in all finite types are considered. For a number of natural constructive intepretations, the corresponding predicate logic of modified realizability is proved to be nonarithmetical.

MSC:
03F30 First-order arithmetic and fragments
03C62 Models of arithmetic and set theory
03F50 Metamathematics of constructive systems
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