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arXiv · 2205.08276

Generalized Realizability and Intuitionistic Logic

Aleksandr Yu. Konovalov
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Abstract

Let V be a set of number-theoretical functions. We define a notion of V -realizability for predicate formulas in such a way that the indices of functions in V are used for interpreting the implication and the universal quantifier. In this paper we prove that Intuitionistic Predicate Calculus is sound with respect to the semantics of V -realizability if and only if some natural conditions for V hold.

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Aleksandr Yu. Konovalov. 2022-05-17. Generalized Realizability and Intuitionistic Logic. https://arxiv.org/abs/2205.08276

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