2007 Fiscal Year Final Research Report Summary
Ideals on P_κλ considered from the point of view of the relation with large cardinals axioms and the generalized continuum hypothesis
| Project/Area Number |
18540143
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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 | Kanagawa University |
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Principal Investigator |
ABE Yoshihiro Kanagawa University, Faculty of Engineering, Professor (10159452)
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| Co-Investigator(Kenkyū-buntansha) |
KAMO Shizuo University of Osaka Prefecture, Faculty of Science, Professor (30128764)
SHIOYA Masahiro University of Tsukuba, Graduate School of Pure and Applied Sciences, Fulltime Lecturer (30251028)
FUCHINO Sakae Chubu University, Faculty of Engineering, Professor (30292098)
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| Project Period (FY) |
2006 – 2007
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| Keywords | P_κλ / partition property / ineffability / stationary reflection / saturated ideal / fiorcing / club filter / diamond principle |
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| Research Abstract |
(1) We proved that |Pκλ|=λ if κ is mildly λ ineffable and cf(λ)〓κ.
(2) We showed the club filter on Pκλ is weakly presaturated under the Reflection principle.
(3) We showed n is mildly A ineffable Pκ(2^<λ<κ>) has the weak partition property.
(4) We proved every ineffbale subset of Pκλ has the partition property if no cardinal in (κ, λ] is II^2_1-indescribable.
(5) Starting from a model of a huge cardinal we built a simple forcing model in which ω_1 carries an ω_2 saturated ideal.
(6) We extended a theorem of Shelah on the diamond principle in Pω_1λ(◇ω_, λ,) to Pκλ as follows:
(a) ◇_<κ, λ> holds if 2^ω=2^κ with κ<λ
(b) Building upon a model of a supercompact cardinal, we gave a forcing model in which 2^ω=2^κ whereas holds whenever κ< λ.
(7) We got some independence results for cofinality, additivity number, and covering number of the ideal I_f.
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[Journal Article] Diamonds on ρ_kλ
Author(s)
Masahiro Shioya
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Journal Title
Proceedings of Computational Prospects of infinity (in press)(to appear)
Description
「研究成果報告書概要(欧文)」より
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[Presentation] 定常集合の組合せ論2008
Author(s)
塩谷 真弘
Organizer
日本数学会年会(数学基礎論・歴史分科会特別講演)
Place of Presentation
近畿大学
Year and Date
2008-03-25
Description
「研究成果報告書概要(和文)」より
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[Presentation] 強制法入門2007
Author(s)
渕野 昌
Organizer
数学基礎論サマースクール
Place of Presentation
静岡大学
Year and Date
20070904-06
Description
「研究成果報告書概要(和文)」より
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