Research of the structure of proofs in nonstandard models and formal theories
| Project/Area Number |
16K17653
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Kisarazu National College of Technology |
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Principal Investigator |
Kurahashi Taishi 木更津工業高等専門学校, 基礎学系, 講師 (10738446)
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 数理論理学 / 数学基礎論 / 不完全性定理 / 形式的算術 / 証明可能性述語 / 証明可能性論理 / 算術のモデル / 様相論理 / 証明可能性 / 超準モデル |
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| Outline of Final Research Achievements |
Through the syntactic and semantic analysis of provability predicates, I studied the structure and the nature of formal proofs and provability. Through the analysis of provability predicates based on modal logics and arithmetical interpretations, the analysis of structures of formal proofs by constructing nonstandard provability predicates, and the analysis of the second incompleteness theorem, I could have a certain perspective to the situation around the incompleteness theorems.
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| Academic Significance and Societal Importance of the Research Achievements |
証明可能性述語の性質の分析を通じて形式的証明の構造を理解するという研究が Goedel による不完全性定理の証明以降に盛んに行われてきたが，これまで十分には議論されていないような基本的な事項も多い．こうした状況下で，証明可能性述語の基本的な振る舞いについて多角的な視点で根本的な分析をするという研究を行い，一定の成果を得ることができた．これにより形式的体系の証明可能性や証明の構造に関する理解に向けた，ある程度の前進ができたといえる．
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Report
(4 results)
Research Products
(25 results)
