论文标题
PRA中的解释性
Interpretability in PRA
论文作者
论文摘要
在2009年的本文中，我们研究了IL（PRA），即PRA的可解释性逻辑。由于PRA既不是反身理论，也不是可公理的理论，因此两个已知的算术完整性结果不适用于PRA：IL（PRA）不是ILM或ILP。 IL（PRA）当然包含所有已知的原则，即IL（ALL）的一部分，这是所有合理算术理论所共有的原理的解释性逻辑。在本文中，我们采用了PRA的两个算术特性，并查看它们在模态逻辑IL（PRA）中的后果是什么。这些属性反映在所谓的Beklemishev原理B中，而Zambella的原理Z，这两个原理都不是IL的一部分（ALL）。两种原则及其相互关系都被提交了模态研究。特别是，我们证明了B的框架条件。此外，我们证明了Z遵循B的限制形式B。最后，我们概述了IL（PRA）与重要的其他介意性原则的已知关系。
In this paper from 2009 we study IL(PRA), the interpretability logic of PRA. As PRA is neither an essentially reflexive theory nor finitely axiomatizable, the two known arithmetical completeness results do not apply to PRA: IL(PRA) is not ILM or ILP. IL(PRA) does of course contain all the principles known to be part of IL(All), the interpretability logic of the principles common to all reasonable arithmetical theories. In this paper, we take two arithmetical properties of PRA and see what their consequences in the modal logic IL(PRA) are. These properties are reflected in the so-called Beklemishev Principle B, and Zambella's Principle Z, neither of which is a part of IL(All). Both principles and their interrelation are submitted to a modal study. In particular, we prove a frame condition for B. Moreover, we prove that Z follows from a restricted form of B. Finally, we give an overview of the known relationships of IL(PRA) to important other interpetability principles.
