论文标题
半古典算术中的prenex正常形式定理
Prenex normal form theorems in semi-classical arithmetic
论文作者
论文摘要
Akama等。在一阶算术的背景下，系统地研究了排除中间和相关原则的算术层次结构。在该论文中，他们首先提供了一种正常形式定理，作为其半古典原则的理由，仅限于Prenex公式。但是，他们的证据有一些错误。在本文中，我们提供了简单的反例，对其prenex正常形式定理，然后以适当的方式对其进行修改。此外，我们表征了几种相对于半古典算术的正常形式定理。
Akama et al. systematically studied an arithmetical hierarchy of the law of excluded middle and related principles in the context of first-order arithmetic. In that paper, they first provide a prenex normal form theorem as a justification of their semi-classical principles restricted to prenex formulas. However, there are some errors in their proof. In this paper, we provide a simple counterexample of their prenex normal form theorem, then modify it in an appropriate way. In addition, we characterize several prenex normal form theorems with respect to semi-classical arithmetic.
