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On the Disjunctive Markov Principle

Ulrich Kohlenbach

Studia Logica 103 (6):1313-1317 (2015)

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(1 other version)Δ10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta ^0_1$$\end{document} variants of the law of excluded middle and related principles. [REVIEW]Makoto Fujiwara - 2022 - Archive for Mathematical Logic 61 (7-8):1113-1127.details We systematically study the interrelations between all possible variations of Δ10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta ^0_1$$\end{document} variants of the law of excluded middle and related principles in the context of intuitionistic arithmetic and analysis. Download Export citation Bookmark
(1 other version)$$\Delta ^0_1$$ variants of the law of excluded middle and related principles.Makoto Fujiwara - 2022 - Archive for Mathematical Logic 61 (7):1113-1127.details We systematically study the interrelations between all possible variations of \(\Delta ^0_1\) variants of the law of excluded middle and related principles in the context of intuitionistic arithmetic and analysis. Download Export citation Bookmark
Refining the arithmetical hierarchy of classical principles.Makoto Fujiwara & Taishi Kurahashi - 2022 - Mathematical Logic Quarterly 68 (3):318-345.details 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. Download Export citation Bookmark 1 citation
Some principles weaker than Markov’s principle.Makoto Fujiwara, Hajime Ishihara & Takako Nemoto - 2015 - Archive for Mathematical Logic 54 (7-8):861-870.details We systematically study several principles and give a principle which is weaker than disjunctive Markov’s principle. We also show that the principle is underivable and strictly weaker than MP∨ in certain extensions of the system EL of elementary analysis. Download Export citation Bookmark 5 citations
Interrelation between weak fragments of double negation shift and related principles.Makoto Fujiwara & Ulrich Kohlenbach - 2018 - Journal of Symbolic Logic 83 (3):991-1012.details Download Export citation Bookmark 5 citations

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