Minimum‐sized Infinite Partitions of Boolean Algebras | Zendy

Donald Monk J. | Zendy

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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.

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