A relative of the approachability ideal, diamond and non-saturation
A relative of the approachability ideal, diamond and non-saturation
复制标题
接近理想、钻石和非饱和度的相对关系
DOI：
10.2178/jsl/1278682214
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
A. Rinot
中科院分区：
文献类型：
--
作者：
A. Rinot
设λ为奇异基数。Zeman改进了Shelah以前的一个结果，证明了2λ = λ+意味着对于任何S <$λ+，S <$S常平稳地反射。对集合S <$λ+，引入了弱可逼近理想的正规子理想，记为I[S; λ].我们说理想是胖的，如果它包含一个平稳集。证明了：1.如果I[S; λ]是脂肪，则NSλ +<$S是不饱和的; 2.如果I[S; λ]是胖的，且2λ = λ+，则S成立; 3.这意味着I[S; λ]对于每一个S <$λ+都是胖的，它经常平稳地反射; 4.它与存在一个失败的超紧基数是相对一致的，而I[S; λ]对于每一个经常平稳反射的平稳S <$λ+是胖的。并研究了较强原理。
Abstract Let λ denote a singular cardinal. Zeman, improving a previous result of Shelah, proved that together with 2λ = λ+ implies ⋄S for every S ⊆ λ+ that reflects stationarily often. In this paper, for a set S ⊆ λ+, a normal subideal of the weak approachability ideal is introduced, and denoted by I[S; λ]. We say that the ideal is fat if it contains a stationary set. It is proved: 1. if I[S; λ] is fat, then NSλ + ∣ S is non-saturated; 2. if I[S; λ] is fat and 2λ = λ+, then ⋄S holds; 3. implies that I[S; λ] is fat for every S ⊆ λ+ that reflects stationarily often; 4. it is relatively consistent with the existence of a supercompact cardinal that fails, while I[S; λ] is fat for every stationary S ⊆ λ+ that reflects stationarily often. The stronger principle is studied as well.