2017 Fiscal Year Final Research Report
Forcing Theory and the Size of the Continuum
Project/Area Number |
15K04977
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Foundations of mathematics/Applied mathematics
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Research Institution | Kobe University |
Principal Investigator |
Brendle Jorg 神戸大学, システム情報学研究科, 教授 (70301851)
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Project Period (FY) |
2015-04-01 – 2018-03-31
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Keywords | 数学基礎論 / 集合論 / トポロジー / 測度論 / 強制法 |
Outline of Final Research Achievements |
We investigated the combinatorial structure of the continuum using novel techniques from forcing theory. In particular, we employed techniques like Mathias forcing with a filter and other ccc forcing notions, a sophisticated version of finite support iteration of forcing, matrix iterations of forcing, generalizations of forcing notions on the real numbers to large cardinals etc, to obtain new independence results about the order relationship between cardinal invariants of the continuum, and about sets of real numbers with maximality properties like ultrafilters and maximal almost disjoint families.
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Free Research Field |
集合論
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