| Project/Area Number |
26887045
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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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, その他部局等, 講師 (10738446)
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| Project Period (FY) |
2014-08-29 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥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 / 可証性述語 / 算術の超準モデル / 超準モデル |
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| Outline of Final Research Achievements |
I studied the notions of proofs and provability in formal systems by investigating provability predicates.
1. Syntactical approach: We extended the first and second incompleteness theorems to arithmetically definable theories of arithmetic. This research is a joint work with Professor Kikuchi Makoto (Kobe University). Also I defined the notion that a theory has the Sigma_n disjunction property, and we revealed several properties of this notion.
2. Semantical approach: I studied the structure of proofs in nonstandard models of arithmetic by investigating provability predicates. By this research, our understanding of the structure of proofs in nonstandard models having a proof of 0=1 was deepened. This is also a joint work with Professor Makoto Kikuchi.
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