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arXiv · 2001.08989

Generalized Realizability and Basic Logic

Aleksandr Yu. Konovalov
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Abstract

Let V be a set of number-theoretical functions. We define a notion of absolute V-realizability for predicate formulas and sequents 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 Basic Logic is sound with respect to the semantics of absolute V-realizability if V satisfies some natural conditions.

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Aleksandr Yu. Konovalov. 2020-01-15. Generalized Realizability and Basic Logic. https://arxiv.org/abs/2001.08989

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