The start-up for reverse mathematics from various angles

• Project/Area Number: 25887026
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Japan Advanced Institute of Science and Technology
• Principal Investigator: YOKOYAMA Keita 北陸先端科学技術大学院大学, 情報科学研究科, 助教 (10534430)
• Project Period (FY): 2013-08-30 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000); Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 逆数学 / ２階算術 / 組み合わせ論 / 証明論 / 計算可能性理論 / 数学基礎論 / 2階算術

Outline of Final Research Achievements

The purpose of this research is to develop several new approaches for the study of reverse mathematics, whose goal is to determine the strength of ordinary mathematical theorems from various angles. In this research, I investigated the proof-theoretic strength of several combinatorial principles and introduced several new methods to determine the proof-theoretic strength. I also found a new way to apply these results into the study of termination analysis.

Research Products

• [Journal Article] Categorical characterizations of the nat- ural numbers require primitive recursion (2015)
  • Author(s): Leszek Aleksander Kolodziejczyk and Keita Yokoyama
  • Journal Title: Annals of Pure and Applied Logic Volume: 166 Issue: 2 Pages: 219-231
  • DOI: 10.1016/j.apal.2014.10.003
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] On the Ramseyan factorization theorem (2014)
  • Author(s): S.Murakami, T.Yamazaki and K.Yokoyama
  • Journal Title: Lecture Notes in Computer Science Volume: 8493 Pages: 324-332
  • DOI: 10.1007/978-3-319-08019-2_33
  • NAID: 120005617819
  • ISBN: 9783319080185, 9783319080192
  • Peer Reviewed
• [Journal Article] Nonstandard second-order arithmetic and Riemann’s mapping theorem (2014)
  • Author(s): Yoshihiro Horihata and Keita Yokoyama
  • Journal Title: Annals of Pure and Applied Logic Volume: 165 Issue: 2 Pages: 520-551
  • DOI: 10.1016/j.apal.2013.06.022
  • NAID: 120005425784
  • Peer Reviewed
• [Journal Article] Propagation of partial randomness (2014)
  • Author(s): Kojiro Higuchi, Phil Hudelson, Stephen G. Simpson and Keita Yokoyama
  • Journal Title: Annals of Pure and Applied Logic Volume: 165 Issue: 2 Pages: 742-758
  • DOI: 10.1016/j.apal.2013.10.006
  • NAID: 120005473119
  • Peer Reviewed
• [Journal Article] Reverse mathematics and Peano categoricity (2013)
  • Author(s): Stephen G. Simpson and Keita, Yokoyama
  • Journal Title: Annals of Pure and Applied Logic Volume: 164 Issue: 3 Pages: 284-293
  • DOI: 10.1016/j.apal.2012.10.014
  • Peer Reviewed
• [Presentation] What is needed to characterize the natural number system? (2015)
  • Author(s): Keita Yokoyama
  • Organizer: Constructivizm and Computability 2015
  • Place of Presentation: Siinoki Cultural Complex, Kanazawa, Ishikawa, Japan
  • Year and Date: 2015-03-02 – 2015-03-06
• [Presentation] Reverse mathematics and termination analysis (2015)
  • Author(s): Keita Yokoyama
  • Organizer: 14th Asian Logic Conference
  • Place of Presentation: IIT Bombay, India
  • Year and Date: 2015-01-05 – 2015-01-08
  • Invited
• [Presentation] Termination theorem and Ramsey's theorem (2014)
  • Author(s): Keita Yokoyama
  • Organizer: IMS-JSPS Joint Workshop in Mathematical Logic and Foundations of Mathematics
  • Place of Presentation: National University of Singapore, Singapore
  • Year and Date: 2014-09-01 – 2014-09-05
  • Invited
• [Presentation] Proof transformations for nonstandard analysis (2014)
  • Author(s): Keita Yokoyama
  • Organizer: The 10th AIMS Conference on Dynamical Sys- tems, Differential Equations and Applications, Special session 114: Nonstandard Analysis, Quan- tizations and Singular Perturbations
  • Place of Presentation: Madrid, Spain
  • Year and Date: 2014-07-10
  • Invited
• [Presentation] Use of nonstandard models in reverse mathematics (2014)
  • Author(s): Keita Yokoyama
  • Organizer: Journees sur les Arithmetiques Faibles 33
  • Place of Presentation: University of Gothenburg, Gothenburg, Sweden
  • Year and Date: 2014-06-16 – 2014-06-18
  • Invited
• [Presentation] The strength of Ramsey’s theorem from several different view points (2014)
  • Author(s): Keita Yokoyama
  • Organizer: CORCON2014 Workshop
  • Place of Presentation: Genoa, Italy
  • Year and Date: 2014-03-24 – 2014-03-27
• [Presentation] Finite iterations of infinite and finite Ramsey's theorem (2014)
  • Author(s): Keita Yokoyama
  • Organizer: Computability Theory and Foundations of Mathematics 2014
  • Place of Presentation: Tokyo Institute of Technology, Tokyo, Japan
  • Year and Date: 2014-02-17 – 2014-02-20
• [Remarks] Research map
  • URL: http://researchmap.jp/read0145758/?lang=japanese