New developments in iterated forcing
| Project/Area Number |
18K13448
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 12030:Basic mathematics-related
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| Research Institution | Shizuoka University |
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Principal Investigator |
Mejia Diego 静岡大学, 理学部, 准教授 (70777961)
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2021: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2020: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 強制法理論 / 反復強制法 / Creature forcing / 連続体上の組合せ論 / 超フィルター / 多次元反復強制法 / 強測度ゼロ / Forcing Theory / Forcing Iterations / 自然数上のイデアル / Strong Measure Zero / Real line / Creature Forcing / Bounded Arithmetic / Ultrafilters / Strong Measure Zero Sets / 限定算術 / 連続体上の組合せ |
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| Outline of Final Research Achievements |
During this project, we obtained results that contributed to the development of modern forcing techniques and to the understanding of the combinatorics of the real line. All these are presented in 13 published articles (including 2 preprints), where 12 are in international journals and 6 are in top journal in Mathematics and in Logic. The result that has the most impact is the paper "Cichon's maximum without large cardinal", where we elaborated novel forcing techniques and solved the very deep problem of Cichon's maximum, which describes completely the connections between Lebesgue measure, Baire category and compactness of the irrational numbers. This work is product of active collaboration with researches in Austria and in Israel, which has developed into many publications in high impact journals, including the Journal of the European Mathematical Society.
The results of this project has been disclosed in 16 invited lecture, most of them at international conferences.
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| Academic Significance and Societal Importance of the Research Achievements |
Since the real line is present in all mathematical fields of research, its understanding is a essential part of the development of sciences. The research achievements of this projects provides great contribution to its understanding, supported by international collaboration.
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Report
(6 results)
Research Products
(43 results)
