Refining the arithmetical hierarchy of classical principles

2022/06/09 by Makoto Fujiwara, Taishi Kurahashi · 1 voice · 1 citation
Computer Science · #Computability, Logic, AI Algorithms #Logic, programming, and type systems #semigroups and automata theory

paper · doi:10.1002/malq.202000077

openalex publication_date 2022/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

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.

Citations

• Markov's principle, Church's thesis and Lindelöf's theorem

Cited by

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

Discussions

• … Il y a aussi un travail ultérieur, Fujiwara et Kurahashi, “Refining the arithmetical hierarchy of classical principles” doi.org/10.1002/malq... (= arxiv.org/abs/2010.11527 ) qui n'est pas forcément [bsky, 0 points, 1 comments]