Deepening of the research in set-theoretic topology with forcing and large cardinal properties

2017 Fiscal Year Final Research Report

• Project/Area Number: 25400207
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Osaka Prefecture University
• Principal Investigator: Kada Masaru 大阪府立大学, 理学(系)研究科(研究院), 准教授 (00312447)
• 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)
• Research Collaborator: Iwasa Akira ; Kamo Shizuo ; Kato Takuto ; Shizuma Souji
• Project Period (FY): 2013-04-01 – 2018-03-31
• 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

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.

Free Research Field

数理論理学