Construction of models of higher Chang conjectures and saturated ideals
| Project/Area Number |
23540119
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | University of Tsukuba |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
ABE Yoshihiro 神奈川大学, 理学部, 教授 (10159452)
MATSUBARA Yo 名古屋大学, 情報文化学部, 教授 (30242788)
TSUBOI Akito 筑波大学, 数理物質系, 教授 (30180045)
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| Project Period (FY) |
2011 – 2013
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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: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 数理論理学 / 公理的集合論 / 無限組合せ論 / 巨大基数 / 強制法 / 反映原理 / 飽和イデアル / 稠密イデアル |
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| Research Abstract |
1. On the construction of a model in which higher Chang conjecture holds. Foreman constructed a model in which Chang conjecture holds for triples, but the case for quadruples remains open. As the first step toward the solution, we gave a much simpler construction of a model like Foreman's.
2. On the construction of a model that contains a saturated ideal. Woodin constructed a model that contains a dense ideal, but the corresponding Boolean algebra is not yet known. As the first step toward the solution, we constructed by two-step iterated forcing, a model that contains a strongly saturated ideal originally due to Laver, and that contains a centered ideal originally due to Laver and Foreman.
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Report
(4 results)
Research Products
(12 results)
