## Abstract In this article we investigate the dual‐shattering cardinal ℌ, the dual‐splitting cardinal 𝔖 and the dual‐reaping cardinal 𝔎, which are dualizations of the well‐known cardinals 𝔥 (the shattering cardinal, also known as the distributivity number of __P__(ω)/fin), __s__ (the splitting num
Around splitting and reaping for partitions ofω
✍ Scribed by Hiroaki Minami
- Publisher
- Springer
- Year
- 2010
- Tongue
- English
- Weight
- 301 KB
- Volume
- 49
- Category
- Article
- ISSN
- 0933-5846
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## Abstract We prove that all algebras __P__(__w__)__/I__~R~, where the __I__~R~‐'s are ideals generated by partitions of W into finite and arbitrary large elements, are isomorphic and homogeneous. Moreover, we show that the smallest size of a tower of such partitions with respect to the eventually