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Applications of forcing in bounded arithmetic

Research Project

Project/Area Number 18K03400
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 12030:Basic mathematics-related
Research InstitutionGunma Prefectural Women's University

Principal Investigator

Kuroda Satoru  群馬県立女子大学, 文学部, 教授 (30300586)

Project Period (FY) 2018-04-01 – 2024-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords限定算術 / 計算量理論 / 超準モデル / 算術モデル / 証明の複雑さ / 線形代数学 / 強制法 / 組み合わせ論
Outline of Final Research Achievements

In this research, we reformulate the theory of forcing on nonstandard models of bounded arithmetic which was first developed by Gaisi Takeuti and HIromasa Yasumoto and extend the relation between generic models and polynomial time computable classes to its subclasses.
We also extend the theory to treat the satisfiability of the strength of formulas and as a consequence, we gave a condition on which a version of pigeonhole principle is satisfied in generic extensions.
Moreover, we considered the provability of propositions of linear algebra which aims to find candidate independent statements.

Academic Significance and Societal Importance of the Research Achievements

本研究において得られた結果は,限定算術におけるモデルの考察に新たな視点と方法を与えるものであり,必ずしも体系的な方法が与えられていなかったこの分野に大きく貢献するものである.
また,ここで得られた計算量クラスと限定算術体系との関係は,理論計算機科学においてもいくつかの示唆を与えており,複合的な分野にまたがった貢献が期待される.

Report

(7 results)
  • 2023 Annual Research Report   Final Research Report ( PDF )
  • 2022 Research-status Report
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (6 results)

All 2023 2022 2021 2019

All Journal Article (1 results) (of which Peer Reviewed: 1 results) Presentation (5 results) (of which Int'l Joint Research: 2 results,  Invited: 1 results)

  • [Journal Article] Takeuti-Yasumoto Forcing Revisited2022

    • Author(s)
      Satoru Kuroda
    • Journal Title

      Proceedings of the 9th International Conference on Computability Theory and Foundations of Mathematics

      Volume: 1 Pages: 123-155

    • DOI

      10.1142/9789811259296_0006

    • Related Report
      2022 Research-status Report
    • Peer Reviewed
  • [Presentation] Provability of matrix properties in formal theories of linear algebra2023

    • Author(s)
      黒田覚
    • Organizer
      RIMS共同研究(公開型)「証明論と計算論の最前線」
    • Related Report
      2023 Annual Research Report
  • [Presentation] Linera Algebra in Bounded Arithmetic2021

    • Author(s)
      黒田覚
    • Organizer
      証明と計算の理論と応用
    • Related Report
      2021 Research-status Report
  • [Presentation] On Takeuti-Yasumoto forcing2019

    • Author(s)
      Satoru Kuroda
    • Organizer
      Logic Colloquium 2019
    • Related Report
      2019 Research-status Report 2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] Forcing on bounded arithmetic for three sort and related theories2019

    • Author(s)
      黒田覚
    • Organizer
      RIMS共同研究「証明論とその周辺」
    • Related Report
      2019 Research-status Report
  • [Presentation] Forcing in bounded arithmetic for small complexity classes2019

    • Author(s)
      Satoru Kuroda
    • Organizer
      Computability Theory and Foundations of Mathematics 2019
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited

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Published: 2018-04-23   Modified: 2025-01-30  

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