Reverse Mathematics and Models of Arithmetic
Project/Area Number |
19740042
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Single-year Grants |
Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
Research Institution | Tohoku University |
Principal Investigator |
|
Project Period (FY) |
2007 – 2010
|
Project Status |
Completed (Fiscal Year 2010)
|
Budget Amount *help |
¥3,490,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥690,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥500,000 (Direct Cost: ¥500,000)
|
Keywords | 逆数学 / 二階算術 / オメガモデル / 再帰理論 / 帰納的関数論 / オメガ-モデル / ランダム / オメガーモデル / 超準モデル / 弱ケーニッヒの補題 |
Research Abstract |
Reverse mathematics is the research program to classify mathematical theorems according to which set existence axioms are needed to prove them. In this poin of view, we got the following three kinds of results: (1) a new method to construct omaga-model and its application to conservativity result; (2) new notions of randomness and new systems corresponding to them; (3) new reverse mathematical results on Discrete Mathematics and Ring Theory.
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Report
(6 results)
Research Products
(14 results)