Refining the arithmetical hierarchy of classical principles

2020/10/22 by Makoto Fujiwara, Fujiwara, Makoto, Taishi Kurahashi +1 · 1 citation
Computer Science · #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems

paper · pdf · doi:10.48550/arxiv.2010.11527

openalex publication_date 2020/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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• Hierarchical formula classes with respect to semi-classical prenex normalization

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