Applications of forcing in bounded arithmetic

2023 Fiscal Year Final Research Report

• Project/Area Number: 18K03400
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 12030:Basic mathematics-related
• Research Institution: Gunma 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
• Keywords: 限定算術 / 計算量理論 / 超準モデル

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.

Free Research Field

数理論理学

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．