We refine the arithmetical hierarchy of various classical principles by finely investigating the derivability relations between these principles over Heyting arithmetic. We mainly investigate some restricted versions of the law of excluded middle, De Morgan's law, the double negation elimination, the collection principle and the constant domain axiom.

中文翻译：

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细化经典原理的算术层次结构

我们通过在 Heyting 算术上仔细研究这些原则之间的可推导关系来改进各种经典原则的算术层次结构。我们主要研究排中律、德摩根定律、双重否定消除、集合原理和恒域公理的一些限制版本。