We show that for every uncountable regular K and every K-complete Boolean algebra B of density 5 K there is a filter F B such that the number of partitions of length < K modulo F is 5 2'". We apply this to Boolean algebras of the form P ( X ) / I , where I is a n-complete K-dense ideal on X .
A note on complete partitions in boolean algebras
β Scribed by Wojciech Sachwanowicz
- Publisher
- John Wiley and Sons
- Year
- 1990
- Tongue
- English
- Weight
- 203 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0044-3050
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## Abstract We characterize complete Boolean algebras with dense subtrees. The main results show that a complete Boolean algebra contains a dense tree if its generic filter collapses the algebra's density to its distributivity number and the reverse holds for homogeneous algebras. (Β© 2006 WILEYβVCH
Three classes of finite structures are related by extremal properties: complete d-partite d-uniform hypergraphs, d-dimensional affine cubes of integers, and families of 2 d sets forming a d-dimensional Boolean algebra. We review extremal results for each of these classes and derive new ones for Bool
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