Generalized Realizability for Extensions of the Language of Arithmetic
A. Yu. Konovalov · Moscow University Mathematics Bulletin · 2019
Let L be an extension of the language of arithmetic, F be a class of number-theoretical functions. A notion of the V -realizability for L -formulas is defined in such a way that indexes of functions in V are used for interpreting the implication and the universal quantifier. It is proved that the semantics for L based on the V -realizability coincides with the classic semantics if and only if V contains all L -definable functions.