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Reconsideration of the relationship between formalism and intuitionism via proof-theoretical method

Research Project

Project/Area Number 22820054
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeSingle-year Grants
Research Field Philosophy/Ethics
Research InstitutionKeio University

Principal Investigator

AKIYOSHI Ryota  慶應義塾大学, 文学研究科, 助教 (20587852)

Project Period (FY) 2010 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords哲学 / 倫理学 / 数学基礎論
Research Abstract

We investigated the relationship between formalism and intuitionism from the view points of mathematical logic and philosophy. In the joint mathematical work with G. Mints(Stanford University), the complete cut-elimination theorem for Omega-rule, which had been an open problem, is proved. In the philosophical work, we analysed the history of proof theory from the viewpoint of "analysis of impredicativity" and presented some issues to be addressed.

Report

(3 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • Research Products

    (18 results)

All 2012 2011 2010 Other

All Journal Article (9 results) (of which Peer Reviewed: 2 results) Presentation (9 results)

  • [Journal Article] 非可述性の分析としての証明論2012

    • Author(s)
      秋吉亮太
    • Journal Title

      科学基礎論研究

      Volume: 第39巻 Pages: 43-57

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] An Extension of the Iterated Omega-Rule2011

    • Author(s)
      Ryota Akiyoshi
    • Journal Title

      CARLS Series of Advanced Study of Logic and Sensibility

      Volume: Vol.5 Pages: 221-230

    • Related Report
      2011 Final Research Report
  • [Journal Article] Analysis and Extension of Omega-Rule2011

    • Author(s)
      Ryota Akiyoshi and Grigori Mints
    • Journal Title

      arXiv

    • URL

      http://arxiv.org/abs/0904.4742

    • Related Report
      2011 Final Research Report
  • [Journal Article] An Ordinal-Free Proof of the Cut-elimination Theorem for Pi^1_1-CA withω-rule2011

    • Author(s)
      Ryota Akiyoshi and Grigori Mints
    • Journal Title

      The Bulletin of Symbolic Logic

      Volume: Volume16 Pages: 293-293

    • Related Report
      2011 Final Research Report
  • [Journal Article] An Extension of the Iterated Omega-Rule2011

    • Author(s)
      Ryota Akiyoshi
    • Journal Title

      CARLS Series of Advance Study of Logic and Sensibility

      Volume: 5 Pages: 221-230

    • Related Report
      2011 Annual Research Report
  • [Journal Article] Analysis and Extension of Omega-Rule2011

    • Author(s)
      Ryota Akiyoshi, Grigori Mints
    • Journal Title

      arXiv(オンラインジャーナル)

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Gentzen's First Consistency Proof Revisited2010

    • Author(s)
      Ryota Akiyoshi
    • Journal Title

      CARLS Series of Advanced Study of Logic and Sensibility

      Volume: Vol.4 Pages: 315-324

    • Related Report
      2011 Final Research Report 2010 Annual Research Report
  • [Journal Article] An Ordinal-Free Proof of the Cutelimination Theorem for II^1_1-CA withω-rule2010

    • Author(s)
      Ryota Akiyoshi, Grigori Mints
    • Journal Title

      Bulletin Symbolic Logic

      Volume: 16 Pages: 293-293

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Complete Cut-Elimination Theorem forΩ-Rule

    • Author(s)
      Ryota Akiyoshi and Grigori Mints
    • Journal Title

      The Bulletin of Symbolic Logic

    • Related Report
      2011 Final Research Report
  • [Presentation] Complete Cut-Elimination Theorem for Ω-Rule2011

    • Author(s)
      R.Akiyoshi, G.Mints
    • Organizer
      Logic Colloquium 2011
    • Place of Presentation
      University of Barcelona
    • Year and Date
      2011-07-11
    • Related Report
      2011 Annual Research Report
  • [Presentation] 非可述性の分析としての証明論2011

    • Author(s)
      秋吉亮太
    • Organizer
      2011年度科学基礎論学会ワークショップ「あたらしい数理論理学の揺籃~証明論的な順序数と集合論的順序数」における提題者
    • Place of Presentation
      愛媛大学(招待講演)
    • Year and Date
      2011-06-05
    • Related Report
      2011 Annual Research Report
  • [Presentation] Complete Cut-Elimination Theorem forΩ-Rule2011

    • Author(s)
      Ryota Akiyoshi and Grigori Mints
    • Organizer
      Logic Colloquium 2011
    • Place of Presentation
      University of Barcelona
    • Related Report
      2011 Final Research Report
  • [Presentation] Ω規則の拡張について2011

    • Author(s)
      秋吉亮太
    • Organizer
      第四十四回日本科学哲学会
    • Place of Presentation
      日本大学
    • Related Report
      2011 Final Research Report
  • [Presentation] 非可述性の分析としての証明論2011

    • Author(s)
      秋吉亮太
    • Organizer
      2011年度科学基礎論学会
    • Place of Presentation
      愛媛大学
    • Related Report
      2011 Final Research Report
  • [Presentation] Finite Notations for Omega_mu+1-rule2010

    • Author(s)
      Ryota Akiyoshi
    • Organizer
      Logic Colloquium 2010
    • Place of Presentation
      パリ第七大学
    • Year and Date
      2010-07-27
    • Related Report
      2010 Annual Research Report
  • [Presentation] Introduction to Proof Theory for Impredicative Systems2010

    • Author(s)
      秋吉亮太
    • Organizer
      Logic Seminar
    • Place of Presentation
      東北大学
    • Year and Date
      2010-06-04
    • Related Report
      2010 Annual Research Report
  • [Presentation] Finite Notations forΩ_μ+1-rule2010

    • Author(s)
      Ryota Akiyoshi
    • Organizer
      Logic Colloquium 2010
    • Place of Presentation
      Paris Dederot University
    • Related Report
      2011 Final Research Report
  • [Presentation] ゲンツェンの無矛盾性証明再訪2010

    • Author(s)
      秋吉亮太
    • Organizer
      論理学と数学の哲学の研究会
    • Place of Presentation
      大阪大学
    • Related Report
      2011 Final Research Report 2010 Annual Research Report

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Published: 2010-08-27   Modified: 2016-04-21  

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