A notion of strictly primitive recursive realizability is introduced by Damnjanovic in 1994. It is a kind of constructive semantics of the arithmetical sentences using primitive recursive functions. It is of interest to study the corresponding predicate logic. It was argued by Park in 2003 that the predicate logic of strictly primitive recursive realizability is not arithmetical. Park’s argument is essentially based on a claim of Damnjanovic that intuitionistic logic is sound with respect to strictly primitive recursive realizability, but that claim was disproved by the author of this article in 2006. The aim of this paper is to present a correct proof of the result of Park.

Damnjanovic 在 1994 年引入了严格原始递归可实现性的概念。它是一种使用原始递归函数的算术语句的构造语义。研究相应的谓词逻辑是很有趣的。Park 在 2003 年提出，严格原始递归可实现性的谓词逻辑不是算术的。Park 的论点本质上是基于 Damnjanovic 的主张，即直觉主义逻辑在严格的原始递归可实现性方面是合理的，但该主张在 2006 年被本文作者反驳。本文的目的是提供一个正确的证明朴的结果。