Construction of an interpretation between systems of applicative theory and set theory
| Project/Area Number |
24840022
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Japan Advanced Institute of Science and Technology |
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Principal Investigator |
TAKAKO Nemoto 北陸先端科学技術大学院大学, 情報科学研究科, 助教 (20546155)
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| Project Period (FY) |
2012-08-31 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 集合論 / 演算適用の理論 / 証明論 / 翻訳 / 算術 / applicative theory / proof theory / set theory / interpretation / 数理論理学 |
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| Research Abstract |
We gave an interpretation from set theory, whoes basic objects are sets, into applicative theory, whoes basic objects are operators and natural numbers, by modefing the interpretation method from set theory into type theory, proposed by P. Aczel. It turned out that set theories which can be interpreted by this new method is defferent from ordinal set theory in the following sense: 1. They allows
the existtence of universal set, namely, the set of ALL set; 2. They does not allow rather weak set comperehension axioms. We have constructed an appropreate set theory which can be interpreted by this method in the sense of the proof theoretic strength.
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Report
(3 results)
Research Products
(10 results)
