| Project/Area Number |
24540121
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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 | Nagoya University |
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Principal Investigator |
YOSHINOBU YASUO 名古屋大学, 情報科学研究科, 准教授 (90281063)
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| Co-Investigator(Renkei-kenkyūsha) |
FUCHINO SAKAE 神戸大学, 大学院システム情報学研究科, 教授 (30292098)
MIYAMOTO TADATOSHI 南山大学, 経営学部, 教授 (70229889)
KADA MASARU 大阪府立大学, 大学院理学系研究科, 准教授 (00312447)
TOMOYASU KAZUO 都城工業高等専門学校, 一般科目理科, 准教授 (10332107)
SAKAI HIROSHI 神戸大学, 大学院システム情報学研究科, 准教授 (70468239)
USUBA TOSHIMICHI 早稲田大学, 基幹理工学部, 准教授 (10513632)
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| Research Collaborator |
MATSUBARA YO 名古屋大学, 大学院情報科学研究科, 教授 (30242788)
König Bernhard IDS GmbH, Analysis and Reporting Services
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| Project Period (FY) |
2012-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 数学基礎論 / 公理的集合論 / 強制法 / 集合論的位相空間論 / 強制公理 / バナッハ・マズア型ゲーム |
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| Outline of Final Research Achievements |
In the study of axiomatic set theory, combinatorial properties of infinite cardinals greater than or equal to aleph 2 are less understood than those of smaller cardinals. In this research, we studied invariance of combinatorial properties of relatively small infinite cardinals greater than or equal to aleph 2 under various forcing extensions. As a result, we obtained several significant consequences, mainly about problems to what extent and with what sort of partially ordered sets well-known axioms of set theory called forcing axioms are preserved under forcing extensions.
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