Refining the arithmetical hierarchy of classical principles

Mathematical Logic Quarterly 68 (3):318-345 (2022)
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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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Citations of this work

An Escape From Vardanyan’s Theorem.Ana de Almeida Borges & Joost J. Joosten - 2023 - Journal of Symbolic Logic 88 (4):1613-1638.

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References found in this work

Fragments of Heyting arithmetic.Wolfgang Burr - 2000 - Journal of Symbolic Logic 65 (3):1223-1240.
Some principles weaker than Markov’s principle.Makoto Fujiwara, Hajime Ishihara & Takako Nemoto - 2015 - Archive for Mathematical Logic 54 (7-8):861-870.
On the Disjunctive Markov Principle.Ulrich Kohlenbach - 2015 - Studia Logica 103 (6):1313-1317.

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