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Rudin‐Keisler Posets of Complete Boolean Algebras
Author(s) -
Jipsen Peter,
Pinus Alexander,
Rose Henry
Publication year - 2001
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 - 10.1002/1521-3870(200111)47:4<447::aid-malq447>3.0.co;2-w
Subject(s) - partially ordered set , mathematics , boolean algebras canonically defined , stone's representation theorem for boolean algebras , complete boolean algebra , boolean algebra , free boolean algebra , two element boolean algebra , boolean function , combinatorics , discrete mathematics , pure mathematics , algebra over a field , algebra representation
The Rudin‐Keisler ordering of ultrafilters is extended to complete Boolean algebras and characterised in terms of elementary embeddings of Boolean ultrapowers. The result is applied to show that the Rudin‐Keisler poset of some atomless complete Boolean algebras is nontrivial.