A Note on Boolean Algebras with Few Partitions Modulo some Filter

✍ Scribed by Markus Huberich

• Publisher: John Wiley and Sons
• Year: 1996
• Tongue: English
• Weight: 161 KB
• Volume: 42
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.19960420114

✦ Synopsis

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 .