Large cardinal properties of ideals
Large cardinal properties of ideals
批准号:
15540115
负责人:
MATSUBARA Yo
金额:
$1.92万
依托单位:
依托单位国家:
日本
项目类别:
Grant-in-Aid for Scientific Research (C)
财政年份:
2003
资助国家:
日本
项目状态:
已结题
起止时间:
2003 至 2004
关键词:
中文摘要
For X?P_κλ,if|{t∈X:sup(T)=δ}|<;2^<;|δ|>;holds for everyδ<;λ,then we say that X is skinny.Let NS_<;κλ>;denote the non-stationary ideal over P_κλ。For X?P_κλdefine the ideal NS_<;κλ>;|X as follows;\Y?P_κλ(Y∈NS_<;κλ>;|X×X^Y∈NS_<;κλ>;).Y.Matsubara proved that if NS_<;κλ>;|X is precipitous then X has a skinny stationary subset of X·Previously Y.Matsubara and S.Shelah proved that ifλis a strong limit singular cardinal,then there is no skinny stationary subset of P_κλ.Therefore we can conclude that ifλis a strong limit singular cardinal,then NS_<;κλ>;|X cannot be precipitous for every X?P_κλ.We also proved that assuming GCH belowλthe exence of the precipitous<;Using this we can prove that under GCH the precipitousness of NS_<;κλ>;implies the diamond principle on every stationary subset of{α<;λ|cf(α)<;κ}。Therefore under GCH,the precipitousness of NS_<;κλ>;implies the ideal NS_λ|A cannot be saturated for every A.{α<;λ|cf(α)<;κ}。Here NS_λdenotes the non-stationary ideal overλand NS_λ|A denotes the ideal overλgenerated by NS_λandλ-A·
英文摘要
For X⊆P_κλ, if |{t∈X:sup(t)= δ}|<2^<|δ|> holds for every δ<λ, then we say that X is skinny. Let NS_<κλ> denote the non-stationary ideal over P_κλ. For X⊆P_κλ define the ideal NS_<κλ>|X as follows ; ∀Y⊆P_κλ(Y∈NS_<κλ>|X⇔X∩Y∈NS_<κλ>).Y.Matsubara proved that if NS_<κλ>|X is precipitous then X has a skinny stationary subset of X・Previously Y.Matsubara and S.Shelah proved that if λ is a strong limit singular cardinal, then there is no skinny stationary subset of P_κλ.Therefore we can conclude that if λ is a strong limit singular cardinal, then NS_<κλ>|X cannot be precipitous for every X⊆P_κλ.We also proved that assuming GCH below λ the existence of skinny stationary subset of P_κλ is equivalent to the diamond principle on {α<λ|cf(α)<κ}. Using this we can prove that under GCH the precipitousness of NS_<κλ> implies the diamond principle on every stationary subset of {α<λ|cf(α)<κ}. Therefore under GCH, the precipitousness of NS_<κλ> implies the ideal NS_λ|A cannot be saturated for every A⊆{α<λ|cf(α)<κ}. Here NS_λ denotes the non-stationary ideal over λ and NS_λ|A denotes the ideal over λ generated by NS_λ and λ-A・
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DOI:
10.1002/malq.200410101
发表时间:
2004-01-01
期刊:
MATHEMATICAL LOGIC QUARTERLY
影响因子:
0.3
作者:
[König, B, Yoshinobu, Y]
通讯作者:
Yoshinobu, Y
σ-short Boolean algebras
σ-短布尔代数
DOI:
--
发表时间:
2003
期刊:
Mathematical Logic Quarterly 49・6
影响因子:
--
作者:
[Makoto Ttakahashi, Yasuo Yoshinobu]
通讯作者:
Yasuo Yoshinobu
Makoto Takahashi, Yasuo Yoshinobu: "σ-short Boolean algebras"Mathematical Logic Quarterly. 49・6. 543-549 (2003)
高桥诚、吉伸康雄:“σ-短布尔代数”《数理逻辑季刊》49・6(2003)。
DOI:
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发表时间:
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影响因子:
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作者:
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通讯作者:
Masahiro Shioya: "A saturated stationary subset of P_κκ^+"Math.Res.Lett.. 10. 493-500 (2003)
Masahiro Shioya:“P_κκ^+ 的饱和平稳子集”Math.Res.Lett.. 10. 493-500 (2003)
DOI:
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发表时间:
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影响因子:
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作者:
[]
通讯作者:
Yo Matsubara: "Stationary preserving ideals over Pκλ"J.Math.Soc.Japan. 55・3. 827-835 (2003)
Yo Matsubara:“Pκλ 上的稳态保持理想”J.Math.Soc.Japan 55・3(2003)。
DOI:
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共 11 条
Application of ideals for Godel's Program
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批准号:17540110
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项目类别:Grant-in-Aid for Scientific Research (C)
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资助金额:$2.11万
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财政年份:2005
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负责人:MATSUBARA Yo
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依托单位:
Ideals with large cardinal properties
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批准号:13640113
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项目类别:Grant-in-Aid for Scientific Research (C)
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资助金额:$2.11万
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财政年份:2001
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负责人:MATSUBARA Yo
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依托单位:
Computability and polynomial time computability
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批准号:11640112
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项目类别:Grant-in-Aid for Scientific Research (C)
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资助金额:$2.18万
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财政年份:1999
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负责人:MATSUBARA Yo
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依托单位: