5 found
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  1.  10
    On a Relationship Between Gödel's Second Incompleteness Theorem and Hilbert's Program.Ryota Akiyoshi - 2009 - Annals of the Japan Association for Philosophy of Science 17:13-29.
  2.  6
    An Extension of the Omega-Rule.Ryota Akiyoshi & Grigori Mints - 2016 - Archive for Mathematical Logic 55 (3-4):593-603.
    The Ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega $$\end{document}-rule was introduced by W. Buchholz to give an ordinal-free proof of cut-elimination for a subsystem of analysis with Π11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pi ^{1}_{1}$$\end{document}-comprehension. W. Buchholz’s proof provides cut-free derivations by familiar rules only for arithmetical sequents. When second-order quantifiers are present, they are introduced by the Ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega $$\end{document}-rule and some residual cuts are not (...)
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  3.  8
    Proof Theory as an Analysis of Impredicativity.Ryota Akiyoshi - 2012 - Journal of the Japan Association for Philosophy of Science 39 (2):93-107.
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  4.  4
    Reading Gentzen's Three Consistency Proofs Uniformly.Ryota Akiyoshi & Yuta Takahashi - 2013 - Journal of the Japan Association for Philosophy of Science 41 (1):1-22.
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  5.  22
    Tait's Conservative Extension Theorem Revisited.Ryota Akiyoshi - 2010 - Journal of Symbolic Logic 75 (1):155-167.
    This paper aims to give a correct proof of Tait's conservative extension theorem. Tait's own proof is flawed in the sense that there are some invalid steps in his argument, and there is a counterexample to the main theorem from which the conservative extension theorem is supposed to follow. However, an analysis of Tait's basic idea suggests a correct proof of the conservative extension theorem and a corrected version of the main theorem.
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