2005 Fiscal Year Final Research Report Summary
Applications of pcf to ideals on P_κλ and infinitary combinatorics, and independence proof
| Project/Area Number |
16540127
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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, 工学部, 教授 (10159452)
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| Co-Investigator(Kenkyū-buntansha) |
KAMO Shizuo University of Osaka Prefecture, Faculty of Science, Professor, 理学部, 教授 (30128764)
SHIOYA Masahiro University of Tsukuba, Institute of Mathematics, Full-time Lecture, 数理物質科学研究科, 講師 (30251028)
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| Project Period (FY) |
2004 – 2005
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| Keywords | P_κλ / partition property / supercompact / ineffability / stationary reflection / forcing / nonstationary ideal / presaturation |
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| Research Abstract |
(1)We give a simple proof for Kamo's theorem that there exists a normal ultrafilter on P_κλ if κ is λ supercompact.
(2)We show the ideal of the subsets of P_κλ」a without the weak partition property is not κ^+ saturated.
(3)We showed the minimal ideal on P_κλ with the partition property is not λ^+ saturated.
(4)We proved the minimal normal ideal on P_κλ with the partition priperty is a proper extension of the ideal of noncompletely ineffable subsets.
(5)We showed stationary reflection principle for P_κλ fails if ω_1<κ<λ.
(6)We present a forcing model in which, for every regular μ【less than or equal】κ, the restriction of the nonstationary ideal on P_μκ to {x:cf(sup(x))=ω} is weakly presaturated.
(7)We show that the restriction of the nonstationary ideal on P_κ to {x:cf(sup(x))=ω} is weakly presaturated under the σ stationary reflection in P_κ2^2^2^<<κ>.
(8)We give a correct and simple proof for Shelah's theorem that the minimal cardinality of unbounded subset of P_κλ is equal to that of stationary subset.
(9)We prove the existence of a diamond sequence for P_κλ provided that 2^ω=2^<<κ>, and present a forcing model such that P_<ω2>λ carries a diamond sequence whereas 2^ω<2^<ω_1>.
(10)We showed that the additivity of the ideal Ι_f) is not, greater than the bounded number, and the cofinality of Ι_f) is not smaller than the dominating number.
(11)We present a function f∈^ωω such that T_f is not an ideal.
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Research Products
(12 results)
