2011 Fiscal Year Final Research Report
Quotient structures in set theory of the reals
| Project/Area Number |
21540128
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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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 | Kobe University |
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Principal Investigator |
JORG Brendle 神戸大学, 大学院・システム情報学研究科, 准教授 (70301851)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 数学基礎論 / 集合論 / トポロジー / 測度論 / 強制法の理論 / 組合せ論的集合論 / 記述集合論 |
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| Research Abstract |
We investigated the continuum and its subsets from the point of view of combinatorial and descriptive set theory. In particular, using forcing theory, which is the main method for obtaining independence results in set theory, and other techniques, we focused on combinatorial properties of quotient structures in set theory, like Boolean algebras of the form P(ω)/I where I is a definable ideal on the power set P(ω) of the natural numbersω.
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