Applications of pcf to ideals on P_κλ and infinitary combinatorics, and independence proof

PCF 在 P_κλ 理想和无穷组合学中的应用以及独立性证明

• 批准号: 16540127
• 负责人: ABE Yoshihiro
• 金额: $ 0.96万
• 依托单位: Kanagawa University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16540127/
• 关键词: P_κλ; partition property; supercompact; ineffability; stationary reflection; forcing; nonstationary ideal; presaturation; reflection; 正規極大フィルター; unbounded set; stationary set; saturation

(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.

(1)We给出了卡莫关于P_κλ上存在正规超滤子的定理的一个简单证明. (2)We证明了不具有弱分划性质的P_κλ“a的子集的理想不是κ^+饱和的. (3)We证明了P_κλ上具有配分性质的极小理想不是λ^+饱和的. (4)We证明了P_κλ上具有分划性质的极小正规理想是非完全不可言子集理想的真扩张。(5)We当ω_1<κ<λ时，P_κλ的平稳反射原理失效。(6)We本文提出了一个强迫模型，其中对任意正则μ[小于或等于]κ，P_μκ上的非平稳理想对{x：cf（sup（x））=ω}的限制是弱预饱和的. (7)We证明了在P_κ2^2^2^<<κ>中的σ平稳反射下，P_κ上的非平稳理想对{x：cf（sup（x））=ω}的限制是弱预饱和的. (8)We给出了P_κλ的无界子集的最小基数与平稳子集的最小基数相等的Shelah定理的一个正确而简单的证明。(9)We证明了当2^ω=2^<κ>时，P_κλ存在一个菱形序列，并给出了一个强迫模型，使得P_<ω2>λ带有一个菱形序列，而2^ω<2^<ω_1>.（10）证明了理想l_f）的可加性不大于有界数，且l_f）的共尾性不小于控制数。（11）给出一个函数f∈^ωω，使得T_f不是理想。

项目成果

An ultrafilter with property 6

具有特性 6 的超滤器

• 发表时间: 2006
• 期刊: Proceedings of the American Mathematical Society 134・6
• 作者: M.Yamada;O.Nakata;M.Watanabe;F.Yanase;S.Akashi;S.Akashi;Masahiro Shioya;Masahiro Shioya
• 通讯作者: Masahiro Shioya

Notes on subtlety and ineffability in P_kλ

关于 P_kλ 中微妙和不可言喻的注释

• 发表时间: 2005
• 期刊: Archive for Mathematical Logic 44.5
• 作者: M.Yamada;O.Nakata;M.Watanabe;F.Yanase;S.Akashi;S.Akashi;Masahiro Shioya;Masahiro Shioya;Yoshiniro abe
• 通讯作者: Yoshiniro abe

An ultrafilter with property σ.

具有 σ 属性的超滤器。

• 发表时间: 2006
• 期刊: Proc.Amer.Math.Soc. 134
• 作者: Saharon Shelah;Masahiro Shioya;Masahiro Shioya
• 通讯作者: Masahiro Shioya

An ultrafilter with preperty 6

具有 Preperty 6 的超滤器

• 发表时间: 2006
• 期刊: Proceedings of the American Mathematical Society 134.6
• 作者: 牧野 唯;木村 敦;前垣内賢太郎;鈴木 理;Tadahito Harima;Masahiro Shioya
• 通讯作者: Masahiro Shioya

Diamonds on Pkλ

Pkλ 上的钻石

• 发表时间: 2008
• 期刊: Lect, Notes. Ser. Inst, Math. Sci 15
• 作者: Shioya;Masahiro
• 通讯作者: Masahiro