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The start-up for reverse mathematics from various angles

Research Project

Project/Area Number 25887026
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeSingle-year Grants
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionJapan 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 *help
¥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.

Report

(3 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Annual Research Report
  • Research Products

    (13 results)

All 2015 2014 2013 Other

All Journal Article (5 results) (of which Peer Reviewed: 5 results,  Acknowledgement Compliant: 1 results) Presentation (7 results) (of which Invited: 4 results) Remarks (1 results)

  • [Journal Article] Categorical characterizations of the nat- ural numbers require primitive recursion2015

    • 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

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] On the Ramseyan factorization theorem2014

    • 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
    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Nonstandard second-order arithmetic and Riemann’s mapping theorem2014

    • 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

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Propagation of partial randomness2014

    • 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

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Reverse mathematics and Peano categoricity2013

    • 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

    • Related Report
      2013 Annual Research Report
    • 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
    • Related Report
      2014 Annual Research Report
  • [Presentation] Reverse mathematics and termination analysis2015

    • Author(s)
      Keita Yokoyama
    • Organizer
      14th Asian Logic Conference
    • Place of Presentation
      IIT Bombay, India
    • Year and Date
      2015-01-05 – 2015-01-08
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Termination theorem and Ramsey's theorem2014

    • 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
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Proof transformations for nonstandard analysis2014

    • 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
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Use of nonstandard models in reverse mathematics2014

    • 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
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] The strength of Ramsey’s theorem from several different view points2014

    • Author(s)
      Keita Yokoyama
    • Organizer
      CORCON2014 Workshop
    • Place of Presentation
      Genoa, Italy
    • Year and Date
      2014-03-24 – 2014-03-27
    • Related Report
      2013 Annual Research Report
  • [Presentation] Finite iterations of infinite and finite Ramsey's theorem2014

    • 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
    • Related Report
      2013 Annual Research Report
  • [Remarks] Research map

    • URL

      http://researchmap.jp/read0145758/?lang=japanese

    • Related Report
      2014 Annual Research Report 2013 Annual Research Report

URL: 

Published: 2013-09-12   Modified: 2016-06-03  

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