Deepening of the research in set-theoretic topology with forcing and large cardinal properties
| Project/Area Number |
25400207
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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 |
Foundations of mathematics/Applied mathematics
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| Research Institution | Osaka Prefecture University |
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Principal Investigator |
Kada Masaru 大阪府立大学, 理学(系)研究科(研究院), 准教授 (00312447)
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| Co-Investigator(Renkei-kenkyūsha) |
Yoshinobu Yasuo 名古屋大学, 情報科学研究科, 准教授 (90281063)
Tomoyasu Kazuo 都城工業高等専門学校, 一般科目, 准教授 (10332107)
Fuchino Sakaé 神戸大学, システム情報学研究科, 教授 (30292098)
Usuba Toshimichi 早稲田大学, 理工学術院, 准教授 (10513632)
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| Research Collaborator |
Iwasa Akira
Kamo Shizuo
Kato Takuto
Shizuma Souji
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| Project Period (FY) |
2013-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 集合論 / 位相空間論 / 強制法 / 巨大基数公理 / 数理論理学 / 無限組合せ論 / 巨大基数 / コンパクト化 / 選択公理 / 公理的集合論 / 基数不変量 / 和集合公理 / 国際情報交換（アメリカ） / 国際情報交換 |
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| Outline of Final Research Achievements |
After the start of this project, several non-academic difficulties for research activities happened, which caused the delay of the project and brought less results than I expected. In particular, I could not get a significant progress in the field of general topology using the set-theoretic method of large cardinal properties, which was one of the main topic I mentioned in the proposal. However, I got several meaningful results in the field of set theory and general topology, including the following topics: (i) Convergence of a sequence to a set after forcing extensions, (ii) Interplay among variants of the axiom of choice when we discard the axiom of union, and (iii) Generalizations of hat-guessing games into infinitary combinatorics.
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Report
(6 results)
Research Products
(14 results)
