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A Note on Boolean Algebras with Few Partitions Modulo some Filter
Author(s) -
Huberich Markus
Publication year - 1996
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19960420114
Subject(s) - mathematics , modulo , ideal (ethics) , complete boolean algebra , uncountable set , mathematics subject classification , two element boolean algebra , free boolean algebra , boolean algebra , stone's representation theorem for boolean algebras , boolean function , filter (signal processing) , discrete mathematics , ultrafilter , combinatorics , boolean algebras canonically defined , parity function , boolean expression , algebra over a field , pure mathematics , algebra representation , computer science , philosophy , countable set , epistemology , computer vision
We show that for every uncountable regular κ and every κ‐complete Boolean algebra B of density ≤ κ there is a filter F ⊆ B such that the number of partitions of length < modulo κ F is ≤2 <κ . We apply this to Boolean algebras of the form P(X) / I , where I is a κ‐complete κ‐dense ideal on X. Mathematics Subject Classification: 06E05, 03C20.
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