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Minimum‐sized Infinite Partitions of Boolean Algebras
Author(s) -
Donald Monk J.
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.19960420142
Subject(s) - mathematics , complete boolean algebra , two element boolean algebra , partition (number theory) , boolean algebras canonically defined , class (philosophy) , stone's representation theorem for boolean algebras , boolean algebra , free boolean algebra , interval (graph theory) , discrete mathematics , mathematics subject classification , property (philosophy) , boolean function , combinatorics , algebra over a field , pure mathematics , filtered algebra , computer science , artificial intelligence , philosophy , epistemology
For any Boolean Algebra A , let c mm ( A ) be the smallest size of an infinite partition of unity in A. The relationship of this function to the 21 common functions described in Monk [4] is described, for the class of all Boolean algebras, and also for its most important subclasses. This description involves three main results: the existence of a rigid tree algebra in which c mm exceeds any preassigned number, a rigid interval algebra with that property, and the construction of an interval algebra in which every well‐ordered chain has size less than c mm . Mathematics Subject Classification: 06E05, 03E05.