| Project/Area Number |
15K17586
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Tokyo Denki University |
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Principal Investigator |
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| Research Collaborator |
Viale Matteo トリノ大学, 数学科, 准教授
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 連続体仮説 / ゲーデルのプログラム / 巨大基数公理 / 強制法公理 / 内部モデル理論 / 記述集合論 / ω_1 の部分集合 / 普遍ベール集合 / 数理論理学 / 集合論 / ω_1の部分集合 |
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| Outline of Final Research Achievements |
In this research, we introduce the notion of universally Baireness for subsets of P(kappa) for an infinite kappa, and characterize this notion in terms of forcings, trees, and generic elementary embeddings. When kappa is equal to omega_1, under the assumptions on large cardinals and inner model theory, we show the following: given an elementary substructure X of V of size omega_1, letting M the Mostowski collapse of X, M is iterable and its iterability is witnessed by a subset of P(omega_1) which universally Baire.
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