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A note on the independence of premiss rule
Mathematical Logic Quarterly 62 (1-2):72-76 (2016)
Abstract
In this note, we prove that certain theories of (many‐sorted) intuitionistic predicate logic are closed under the independence of premiss rule (IPR). As corollaries, we show that and extended by some non‐classical axioms and non‐constructive axioms are closed under IPR.Other Versions
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Citations of this work
A marriage of Brouwer’s intuitionism and Hilbert’s finitism I: Arithmetic.Takako Nemoto & Sato Kentaro - 2022 - Journal of Symbolic Logic 87 (2):437-497.
Some Weak Variants of the Existence and Disjunction Properties in Intermediate Predicate Logics.Nobu-Yuki Suzuki - 2017 - Bulletin of the Section of Logic 46 (1/2).
On the independence of premiss axiom and rule.Hajime Ishihara & Takako Nemoto - 2020 - Archive for Mathematical Logic 59 (7-8):793-815.
References found in this work
Syntactic translations and provably recursive functions.Daniel Leivant - 1985 - Journal of Symbolic Logic 50 (3):682-688.
Some principles weaker than Markov’s principle.Makoto Fujiwara, Hajime Ishihara & Takako Nemoto - 2015 - Archive for Mathematical Logic 54 (7-8):861-870.
A Note on the Godel-Gentzen Translation.Hajime Ishihara - 2000 - Mathematical Logic Quarterly 46 (1):135-138.
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