Ideals on P\kappa\lambda which does not depend on large cardinals
| Project/Area Number |
23540167
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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 | Kanagawa University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
USUBA Toshimichi 神戸大学, 自然科学系, 助教 (10513632)
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| Co-Investigator(Renkei-kenkyūsha) |
KAMO Shizuo 大阪府立大学, 理学部, 名誉教授 (30128764)
SHIOYA Masahiro 筑波大学, 数理物質系, 准教授 (30251028)
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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 | Pκλ / イデアル / unbounded set / Rudin-Keisler ordering / P-point / Q-point / selective ideal / 弱正規イデアル / selective イデアル / stationary set / Bounded イデアル / 非有界集合 / 到達不能基数 / 濃度 / Ｐκλ / 有界集合 / 上限関数 / 双対フィルター / 強到達不能基数 |
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| Research Abstract |
The basic concepts of the structural theory of ideals on P_{\kappa}\lambda, P-points, Q-points, and selective ideals are defined, and several theorems are proved, some of which hold similarly for ideals on \kappa, whereas the others are very different from those on \kappa. We get several facts which says that some theorems on \kappa result from the special situation that \kappa=\lambda.
It has been long known that the stationary sets of P_{\kappa}\lambda reflects when \kappa is supercompact. We construct a forcing model in which \kappa is strongly compact and P_{\kappa}\lambda has a stationary set without such reflection.
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Report
(4 results)
Research Products
(50 results)
