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.

中文翻译：

---

算术语言扩展的广义可实现性

令L为算术语言的扩展，F为一类数论函数。所述的概念V为-realizability大号-formulas以这样的方式，在功能索引定义V是用于解释含义和通用量词。证明了当且仅当V包含所有L可定义的函数时，基于V可实现性的L的语义与经典语义一致。