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Refining the arithmetical hierarchy of classical principles
Author(s) -
Fujiwara Makoto,
Kurahashi Taishi
Publication year - 2022
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.202000077
Subject(s) - mathematics , arithmetic function , axiom , hierarchy , negation , law of excluded middle , domain (mathematical analysis) , algebra over a field , arithmetic , calculus (dental) , pure mathematics , discrete mathematics , epistemology , computer science , law , mathematical analysis , philosophy , medicine , geometry , dentistry , political science , programming language
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.