Generalized Realizability and Intuitionistic Logic
Logic
2022-05-18 v1
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.
Keywords
Cite
@article{arxiv.2205.08276,
title = {Generalized Realizability and Intuitionistic Logic},
author = {Aleksandr Yu. Konovalov},
journal= {arXiv preprint arXiv:2205.08276},
year = {2022}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2001.08989