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2008 Fiscal Year Final Research Report

Investigation on epsilon substitution methods

Research Project

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Project/Area Number 17540115
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKobe University

Principal Investigator

ARAI Toshiyasu  Kobe University, 大学院工学研究科, 教授 (40193049)

Project Period (FY) 2005 – 2008
Keywords証明論
Research Abstract

イプシロン代入法に関しては、帰納的マーロ順序数と弱コンパクト基数の帰納的類似物について研究を行った。その他、証明論全般についての考察や計算量理論と関連する研究も行った。

  • Research Products

    (32 results)

All 2009 2008 2007 2006 2005 Other

All Journal Article (11 results) (of which Peer Reviewed: 11 results) Presentation (21 results)

  • [Journal Article] Non-elementary speed-ups in logic calculi2008

    • Author(s)
      T. Arai
    • Journal Title

      Mathematical Logic Quarterly vol. 6

      Pages: 629-640

    • Peer Reviewed
  • [Journal Article] Polynomial-size Frege proofs of Bollob\'as' theorem on the trace of sets2008

    • Author(s)
      A. Nozaki, T. Arai and N.H. Arai
    • Journal Title

      Proceedings of the Japan Academy Ser. A, vol. 84

      Pages: 159-161

    • Peer Reviewed
  • [Journal Article] Iterating the recursively Mahlo operations, to appear in the proceedings of Logic Methodology2007

    • Author(s)
      T. Arai
    • Journal Title

      Philosophy of Science

      Pages: 0

    • Peer Reviewed
  • [Journal Article] 無矛盾性証明について2007

    • Author(s)
      新井 敏康
    • Journal Title

      科学基礎論研究 第107号

      Pages: 43-51

    • Peer Reviewed
  • [Journal Article] Epsilon substitution method for $\Pi^{0}_{2}$-FIX2006

    • Author(s)
      T. Arai,
    • Journal Title

      Journal of Symbolic Logic vol. 71

      Pages: 1155-1188

    • Peer Reviewed
  • [Journal Article] Proofs of Termination of Rewrite Systems for Polytime Functions2005

    • Author(s)
      T. Arai and G. Moser
    • Journal Title

      Lecture Notes in Computer Science vol. 3821

      Pages: 529-540

    • Peer Reviewed
  • [Journal Article] Epsilon substitution method for $[\Pi^{0}_{1},\Pi^{0}_{1}]$-FIX2005

    • Author(s)
      T. Arai
    • Journal Title

      Archive for Mathematical Logic vol. 44

      Pages: 1009-1043

    • Peer Reviewed
  • [Journal Article] Ideas in the epsilon substitution method for $\Pi^{0}_{1}$-FIX2005

    • Author(s)
      T. Arai
    • Journal Title

      Annals of Pure and Applied Logic vol. 136

      Pages: 3-21

    • Peer Reviewed
  • [Journal Article] Hilbert の第2問題に関する証明論の展開2005

    • Author(s)
      新井 敏康
    • Journal Title

      数学 第57巻

      Pages: 113-126

    • Peer Reviewed
  • [Journal Article] A new function algebra of EXPTIME functions by safe nestedrecursion, to appear in ACM Transactions on Computational Logic(ToCL).

    • Author(s)
      T. Arai and N. Eguchi
    • Pages
      0
    • Peer Reviewed
  • [Journal Article] Intuitionistic fixed point theories over Heyting arithmetic, to appear in a volume of Mintsfest.

    • Author(s)
      T. Arai
    • Pages
      0
    • Peer Reviewed
  • [Presentation] Intuitionistic fixed point theories2009

    • Author(s)
      新井 敏康
    • Organizer
      日本数学会年会
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-26
  • [Presentation] Polysize Frege proofs of Bollob\'as' theorem2009

    • Author(s)
      野崎 昭弘, 新井 敏康, 新井 紀子
    • Organizer
      日本数学会年会
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-26
  • [Presentation] Proofs and sets, An Invited talk at the International Workshop on Constructivism2008

    • Author(s)
      T. Arai
    • Organizer
      Logic and Mathematics
    • Year and Date
      2008-05-28
  • [Presentation] 計算による実数の分類2008

    • Author(s)
      新井 敏康
    • Organizer
      計算による数理科学の展開2008 (研究集会)
    • Place of Presentation
      神戸大学
    • Year and Date
      2008-01-11
  • [Presentation] Arai and N. H. Arai, Polynomial-size Frege proofs of Bollob\'as' theorem on the trace of sets2007

    • Author(s)
      A. Nozaki, T. Arai and N. H. Arai
    • Organizer
      JAIST, ALセミナー
    • Year and Date
      2007-09-14
  • [Presentation] Iterating the recursively Mahlo operations2007

    • Author(s)
      T. Arai
    • Organizer
      An Invited talk at the special session of Logic Methodology, Philosophy of Science
    • Place of Presentation
      Beijing
    • Year and Date
      2007-08-14
  • [Presentation] Resolving the reflecting universes2007

    • Author(s)
      T. Arai
    • Organizer
      日本数学会年会
    • Place of Presentation
      埼玉大学
    • Year and Date
      2007-03-27
  • [Presentation] Non-elementary speed-ups in logic calculi2007

    • Author(s)
      新井 敏康
    • Organizer
      本橋信義先生退職記念会
    • Year and Date
      2007-03-26
  • [Presentation] 無矛盾性証明について2006

    • Author(s)
      新井 敏康
    • Organizer
      科学基礎論学会2006年度秋の研究例会
    • Place of Presentation
      慶應大学
    • Year and Date
      2006-11-25
  • [Presentation] Safe nested recursion を使った EXPTIME 関数の特徴づけ2006

    • Author(s)
      T. Arai and N. Eguchi
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2006-09-22
  • [Presentation] Exact bounds on $\epsilon$ process2006

    • Author(s)
      T. Arai
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2006-09-22
  • [Presentation] Limit existence and lexicographic orderings2006

    • Author(s)
      T. Arai
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2006-09-22
  • [Presentation] Resolving the reflecting universes2006

    • Author(s)
      T. Arai
    • Place of Presentation
      Stanford University
    • Year and Date
      2006-02-21
  • [Presentation] Resolving the reflecting universes2006

    • Author(s)
      T. Arai
    • Organizer
      Berkeley Logic Colloquium
    • Place of Presentation
      University of California, Berkeley
    • Year and Date
      2006-02-17
  • [Presentation] A path ordering POP2005

    • Author(s)
      T. Arai and G. Moser,
    • Year and Date
      2005-12-12
  • [Presentation] Some results on $\epsilon$ calculi2005

    • Author(s)
      T. Arai
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      岡山大学
    • Year and Date
      2005-09-19
  • [Presentation] A path order POP and its applications2005

    • Author(s)
      T. Arai and G. Moser
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      岡山大学
    • Year and Date
      2005-09-19
  • [Presentation] A path order POP and its applications2005

    • Author(s)
      T. Arai and G. Moser
    • Organizer
      JAIST, ALセミナー
    • Year and Date
      2005-09-06
  • [Presentation] 証明論入門一歩前2005

    • Author(s)
      新井 敏康
    • Organizer
      神戸大学理学部数学科談話会
    • Year and Date
      2005-07-14
  • [Presentation] An expository survey on epsilon substitution method

    • Author(s)
      T. Arai
    • Organizer
      An Invited talk at the special session of Logic and Computing, AMC
    • Place of Presentation
      Singapore
  • [Presentation] Tierd recursion and strategies,

    • Author(s)
      T. Arai and G. Moser
    • Organizer
      5th International Workshop on Reduction Strategies in Rewriting and Programming
    • Place of Presentation
      Nara

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Published: 2010-06-10   Modified: 2016-04-21  

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