2010 Fiscal Year Final Research Report
Infinite combinatorial principles and compact cardinals
| Project/Area Number |
20540142
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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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 |
ABE Yoshihiro Kanagawa University, 工学部, 教授 (10159452)
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| Co-Investigator(Kenkyū-buntansha) |
HIRATAYA Sushi 神奈川大学, 工学部, 非常勤講師 (70375400)
USUBA Toshimichi 名古屋大学, 高等研究院, 特任助教 (10513632)
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| Co-Investigator(Renkei-kenkyūsha) |
KAMO Shizuo 大阪府立大学, 理学部, 教授 (30128764)
SHIOYAMA Sahiro 筑波大学, 数理物質科学研究科, 准教授 (30251028)
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| Project Period (FY) |
2008 – 2010
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| Keywords | Pκλ / ineffability / 分割の性質 / stationary set / コンパクト基数 / cofinality / イデアル / reflection |
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| Research Abstract |
We proved several facts in the combinatorial set theory on Pκλ={x⊂λ:|x|<κ}, the set of all subsets of λ with cardinality less than κ. For instance :
(1) If the cofinality ofλis smaller thanκ, then there exists a stationary subset S of Pκλsuch that every stationary subset of S can be splitted intoλ^+many disjoint stationary sets.
(2) If the cofinality ofλis not smaller thanκand there is a weakly normal ideal onPκλ, then the cardinality of PκλisMax(2^<κ,λ).
(3) Suppose that the cofinality ofλis not smaller thanκand X is a subset ofPκλ. Then, X is ineffable if and only if it has the partition property.
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