2017 Fiscal Year Final Research Report
Structural properties of ideals over Pk\lambda
| Project/Area Number |
15K04984
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Kanagawa University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
薄葉 季路 早稲田大学, 理工学術院, 准教授 (10513632)
南 裕明 愛知学院大学, 教養部, 講師 (70646885)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Keywords | ideal / Pκλ / the bounded ideal / the non-stationary ideal / Ulam ideal / Rigidity / coherence |
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| Outline of Final Research Achievements |
We developed the theory of structural properties of ideals over Pκλ.
First it was shown that, at the most cases, the ideal isomorphic to the bounded ideal,that is the smallest idal,does not contain the nonstationary ideal, the smallest normal ideal. Second, we define Ulam ideals similar to the case of κ, and show the bounded ideal is not Ulam, and give the characterization of Ulam ideals using the coherence of its extensions.
Last, we study the rigidity of ideals. The relation between the rigid ideals and Ulam ideals have been turned out.
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| Free Research Field |
公理的集合論
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