2010 Fiscal Year Final Research Report
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 |
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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 |
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| Project Period (FY) |
2007 – 2010
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| Keywords | 逆数学 / 二階算術 / オメガモデル / 再帰理論 |
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| 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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