Investigation on epsilon substitution methods

• Project/Area Number: 17540115
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kobe University
• Principal Investigator: ARAI Toshiyasu Kobe University, 大学院工学研究科, 教授 (40193049)
• Project Period (FY): 2005 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥2,740,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥240,000); Fiscal Year 2007: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2006: ¥800,000 (Direct Cost: ¥800,000); Fiscal Year 2005: ¥900,000 (Direct Cost: ¥900,000)
• Keywords: 証明論 / 数学基礎論 / 数理論理学 / 順序数 / イプシロン代入法

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

• [Journal Article] Non-elementary speed-ups in logic calculi (2008)
  • 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 sets (2008)
  • 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 Methodology (2007)
  • Author(s): T. Arai
  • Journal Title: Philosophy of Science Pages: 0-0
  • 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
  • NAID: 10018919332
  • 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 107 Pages: 43-51
  • NAID: 10018919332
  • 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(印刷中)
  • NAID: 10018919332
• [Journal Article] Epsilon substitution method for $\Pi^{0}_{2}$-FIX (2006)
  • Author(s): T. Arai,
  • Journal Title: Journal of Symbolic Logic vol. 71 Pages: 1155-1188
  • Peer Reviewed
• [Journal Article] Epsilon substitution method for II02-FIX (2006)
  • Author(s): T.Arai
  • Journal Title: Journal of Symbolic Logic 41・4 Pages: 1155-1188
• [Journal Article] Proofs of Termination of Rewrite Systems for Polytime Functions (2005)
  • 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 $[\Pi^{0}_{1},\Pi^{0}_{1}]$-FIX (2005)
  • 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 $\Pi^{0}_{1}$-FIX (2005)
  • 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
  • NAID: 10016419271
  • Peer Reviewed
• [Journal Article] deas in the epsilon substitution method for $Pi^{0}_{1}$-FIX (2005)
  • Author(s): Toshiyasu Arai
  • Journal Title: Annals of Pure and Applied Logic 第136巻 Pages: 3-21
• [Journal Article] Epsilon substitution method for $[Pi^{0}_{1},Pi^{0}_{1}]$-FIX (2005)
  • Author(s): Toshiyasu Arai
  • Journal Title: Archive for Mathematical Logic 第44巻 Pages: 1009-1043
• [Journal Article] Proofs of Termination of Rewrite Systems for Polytime Functions (2005)
  • Author(s): Toshiyasu Arai
  • Journal Title: Lecture Notes in Computer Science 第3821巻 Pages: 529-540
• [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
  • NAID: 10016419271
• [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: 0-0
  • Peer Reviewed
• [Journal Article] Intuitionistic fixed point theories over Heyting arithmetic, to appear in a volume of Mintsfest.
  • Author(s): T. Arai
  • Pages: 0-0
  • Peer Reviewed
• [Journal Article] Iterating the recursively Mahlo operations
  • Author(s): Toshiyasu Arai
  • Journal Title: Proceedings of Logic Methodology, Philosophy of Science (掲載決定)
  • Peer Reviewed
• [Journal Article] Non-elementary speed-ups in logic calculi
  • Author(s): Toshiyasu Arai
  • Journal Title: Mathematical Logic Quarterly. (掲載決定)
  • Peer Reviewed
• [Presentation] Intuitionistic fixed point theories (2009)
  • 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' theorem (2009)
  • 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 Constructivism (2008)
  • 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 sets (2007)
  • 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 operations (2007)
  • 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] Iterating the recursively Mahlo operations (2007)
  • Author(s): Toshiyasu Arai
  • Organizer: Logic Methodology, Philosophy of Science
  • Place of Presentation: 北京
  • Year and Date: 2007-08-14
• [Presentation] Resolving the reflecting universes (2007)
  • 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 calculi (2007)
  • 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 $\epsilon$ process (2006)
  • 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 orderings (2006)
  • 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 universes (2006)
  • Author(s): T. Arai
  • Place of Presentation: Stanford University
  • Year and Date: 2006-02-21
• [Presentation] Resolving the reflecting universes (2006)
  • 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 POP (2005)
  • Author(s): T. Arai and G. Moser,
  • Year and Date: 2005-12-12
• [Presentation] Some results on $\epsilon$ calculi (2005)
  • 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 applications (2005)
  • 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 applications (2005)
  • 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
• [Book] 現代思想臨時増刊、総特集ゲーデル(「ゲーデルの無矛盾性証明」執筆) (2007)
  • Author(s): 新井 敏康
  • Total Pages: 254
  • Publisher: 青土社