| Project/Area Number |
15K17587
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Waseda University (2016-2017)
Kobe University (2015) |
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Principal Investigator |
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| Research Collaborator |
Bagaria Joan Universitat de Barcelona, ICREA and Departament de Lògica,Històriai Filosofia de Ciència, professor
Hamkins Joel David The City University of New York, The Graduate Center, professor
Tsaprounis Konstantinos University of the Aegean, Department of Mathematics, posdoc fellow
MATSUBARA Yo 名古屋大学, 大学院情報学研究科, 教授
SAKAI Hiroshi 神戸大学, 大学院システム情報学研究科, 准教授
ISHII Hiromi 筑波大学, 大学院数理物質科学研究科, 大学院生
YAMAURA Naoki 筑波大学, 大学院数理物質科学研究科, 大学院生
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 巨大基数 / 反映原理 / 集合論的多元宇宙論 / 無限組み合わせ論 / 集合論的地質学 / リンデレフ空間 / パラコンパクト空間 / 強制法 / Pκλ |
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| Outline of Final Research Achievements |
On infinitely combinatorics, we obtained various results such as: applications of the unbranching principle to the ideal theory, comparison between cardinals and P_kappa lambda via combinatorial properties, applications of large cardinals to Lindeloef spaces. For the reflection principle, we separated the strong reflection principle from the weak one, and got the characterization of paracompact spaces.
In addition, for the set-theoretic multiverse and the set-theoretic geology, we showed the fundamental theorem that the downward directedness of all ground models. Furthermore, we proved that there exists the minimum ground model if there exists a large cardinal.
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