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The Boolean Prime Ideal Theorem Plus Countable Choice Do Not Imply Dependent Choice
Author(s) -
Howard Paul,
Rubin Jean E.
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.19960420133
Subject(s) - mathematics , countable set , ideal (ethics) , cardinality (data modeling) , boolean prime ideal theorem , discrete mathematics , prime (order theory) , mathematics subject classification , associated prime , combinatorics , computer science , law , data mining , political science
Two Fraenkel‐Mostowski models are constructed in which the Boolean Prime Ideal Theorem is true. In both models, AC for countable sets is true, but AC for sets of cardinality 2 N oand the 2m = m principle are both false. The Principle of Dependent Choices is true in the first model, but false in the second. Mathematics Subject Classification: 03E25, 03E35, 04A25.