Study of the large infinite intrinsic to the small infinite
| Project/Area Number |
19540112
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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 | University of Tsukuba |
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Principal Investigator |
SHIOYA Masahiro University of Tsukuba, 大学院・数理物質科学研究科, 准教授 (30251028)
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| Co-Investigator(Kenkyū-buntansha) |
ABE Yoshihiro 神奈川大学, 工学部, 教授 (10159452)
TSUBOI Akito 筑波大学, 大学院・数理物質科学研究科, 教授 (30180045)
MATSUBARA Yo 名古屋大学, 大学院・情報科学研究科, 教授 (30242788)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2007: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 数学基礎論 / 巨大基数 / 強制法 / 飽和イデアル / 数理論理学 / 集合論 / 無限組合せ論 / フィルタ / 飽和性 / 定常集合 |
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| Research Abstract |
In set theory, combinatorial properties that small infinite sets can have are quite interesting. In particular, Kunen's result is very important that showed the existence of a model in which the smallest infinite cardinal carries a saturated ideal. The construction of Kunen's model was essentially inductive. We have succeeded in constructing a similar model explicitly. Moreover, elaborating the method, we can construct a new model in which Chang's conjecture for triples holds.
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Report
(4 results)
Research Products
(15 results)
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[Presentation] 定常集合の組合せ論2008
Author(s)
塩谷真弘
Organizer
日本数学会年会数学基礎論・歴史分科会 特別講演
Place of Presentation
近畿大学理工学部
Year and Date
2008-03-25
Related Report
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