| Project/Area Number |
19340019
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Tohoku University |
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Principal Investigator |
TANAKA Kazuyuki 東北大学, 大学院・理学研究科, 教授 (70188291)
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| Co-Investigator(Kenkyū-buntansha) |
YAMAZAKI Takeshi 東北大学, 大学院・理学研究科, 准教授 (30336812)
服部 哲弥 東北大学, 大学院・理学研究科, 教授 (10180902)
小澤 正直 東北大学, 大学院・情報科学研究科, 教授 (40126313)
黒田 覚 群馬県立女子大学, 文学部, 准教授 (30300586)
隈部 正博 放送大学, 教養学部, 准教授 (70255173)
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| Co-Investigator(Renkei-kenkyūsha) |
HATTORI Tetsuya 慶應義塾大学, 経済学部, 教授 (10180902)
OZAWA Masanao 名古屋大学, 大学院・情報科学研究科, 教授 (40126313)
SUZUKI Toshio 首都大学東京, 大学院・理学研究院, 准教授 (30235973)
KURODA Satoru 群馬県立女子大学, 文学部, 准教授 (30300586)
KUMABE Masahiro 放送大学, 教養学部, 准教授 (70255173)
KASHIMA Ryo 東京工業大学, 大学院・情報理工学研究科, 准教授 (10240756)
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| Project Period (FY) |
2007 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥17,550,000 (Direct Cost: ¥13,500,000、Indirect Cost: ¥4,050,000)
Fiscal Year 2010: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2009: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2008: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2007: ¥6,110,000 (Direct Cost: ¥4,700,000、Indirect Cost: ¥1,410,000)
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| Keywords | 数学基礎論 / 超準解析 / 計算可能性理論 / ランダム性 / ロジック / 逆数学 / 2階算術 |
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| Research Abstract |
The main purpose of this research is to lay a logical foundation for non-standard arguments, which have been developed in abstract set theory traditionally. Basing non-standard methods on weak subsystems of second order arithmetic connected with computability, we can obtain constructive contents of propositions by such methods. To device non-standard methods for second order arithmetic, we need to investigate their non-standard models, which are indeed sets of reals (infinite sequences). Amongst the sets of reals, many contain many random elements, which we also explore in this study.
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