proof-theoretic investigations of operations on sets
| Project/Area Number |
25400193
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Chiba University |
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Principal Investigator |
Arai Toshiyasu 千葉大学, 大学院理学研究院, 教授 (40193049)
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| Project Period (FY) |
2013-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 証明論 / 数学基礎論 / collapsing |
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| Outline of Final Research Achievements |
We characterized the existence of weakly compact cardinals in terms of iterations of weakly Mahlo operations. We described ZF-provably existing countable ordinals by means of iterations of Mostowski collapsings. We introduced a class of set functions, which are computable in polynomial time, and introduced a theory in which $\Sigma_{1}$-definable functions are exactly polynomial time computable set functions. We showed that intuitionistic fixed point theories over a weak set theory is a conservative extension of the weak set theory. We showed that the wellordering principle of the derivative of a normal function on ordinals is equivalent to the existence of arbitrarily large countable coded $\omega$-models of the normal function. We gave a finitary procedure by which cut inferences are eliminated from derivations for set theory of $\omega_{1}$. We determined a line between predicative and impredicative fragments of the theory of positive elementary inductive definitions.
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Report
(6 results)
Research Products
(21 results)
