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On Two Attempts of Describing Propositional Readability Logic

机译：关于描述命题可读性逻辑的两次尝试

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The study of propositional realizability logic was initiated in the 50th of the last century. Unfortunately, no description of the class of realizable propositional formulas is found up to now. Nevertheless, some attempts of such a description were made. In 1974, the author proved that every known realizable propositional formula has the property that every one of its closed arithmetical instances is deducible in the system obtained by adding Extended Church's Thesis and Markov Principle as axiom schemes to Intuitionistic Arithmetic. Visser calls this system Markov's Arithmetic. In 1990, another attempt of describing the class of realizable propositional formulas was made by Varpakhovskii who proposed a calculus in an extended propositional language and proved that all known realizable propositional formulas are deducible in this calculus. In this article we prove that every propositional formula deducible in Varpakhovskii's calculus has the property that each of its closed arithmetical instances is deducible in Markov's Arithmetic.
机译：命题可实现性逻辑的研究始于上世纪50年代。不幸的是，到目前为止，尚未找到可实现的命题公式类别的描述。然而，进行了这种描述的一些尝试。 1974年，作者证明了每个已知的可实现命题公式都具有以下性质：在将直觉算术添加扩展教堂的论文和马尔可夫原理作为公理方案而获得的系统中，可以推导每个闭合算术实例。维瑟称这个系统为马尔可夫算术。 1990年，Varpakhovskii进行了另一种描述可实现命题公式类别的尝试，他提出了一种扩展的命题语言演算，并证明了所有已知的可实现命题公式都可在该演算中推导。在本文中，我们证明了在Varpakhovskii演算中可推导的每个命题公式都具有以下性质：在Markov算术中可推导其每个闭合算术实例。

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