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 _κ颗心,if | {t∈x: sup (t) =当}| < 2 ^ < |当| > holds for every当<颗心,那么我们说X是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 _κ颗心(y∈ns _<κ颗心>| x←→x同样y∈ns _<κ颗心>). y.matsubara proved that if ns _<κ颗心>| x is precipitous then x has askinny stationary subset of X Previously Y.Matsubara and S.Shelah proved that if λ is a strong limitsingular cardinal,then there is no skinny stationary subset of p_κ λ.Therefore we can conclude that if λ is a stronglimit单一cardinalthenns_ <κλ>|X cannot be precipitous for every X⊆p_ κλ。我们也proved that assuming GCH below λ theexistence 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 thediamond 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 everyA⊆{α<λ|cf(α)<κ}. Here ns_λ denotes the non-stationary ideal over λ and ns_λ |A denotes the ideal overgenerated by ns_λ and λ-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・
期刊论文(16)
专著(0)
科研奖励(0)
会议论文
登录
查看更多内容
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:
--
发表时间:
期刊:
影响因子:
--
作者:
[]
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:
--
发表时间:
期刊:
影响因子:
--
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:
--
发表时间:
期刊:
影响因子:
--
作者:
[]
通讯作者:
共 11 条
Application of ideals for Godel's Program
-
批准号:17540110
-
项目类别:Grant-in-Aid for Scientific Research (C)
-
资助金额:$2.11万
-
财政年份:2005
-
负责人:MATSUBARA Yo
-
依托单位:
Ideals with large cardinal properties
-
批准号:13640113
-
项目类别:Grant-in-Aid for Scientific Research (C)
-
资助金额:$2.11万
-
财政年份:2001
-
负责人:MATSUBARA Yo
-
依托单位:
Computability and polynomial time computability
-
批准号:11640112
-
项目类别:Grant-in-Aid for Scientific Research (C)
-
资助金额:$2.18万
-
财政年份:1999
-
负责人:MATSUBARA Yo
-
依托单位: