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The Boolean Prime Ideal Theorem Plus Countable Choice Do Not Imply Dependent Choice
Mathematical Logic Quarterly 42 (1):410-420 (1996)
Abstract
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 2math image and the 2m = m principle are both false. The Principle of Dependent Choices is true in the first model, but false in the secondOther Versions
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Citations of this work
No Decreasing Sequence of Cardinals in the Hierarchy of Choice Principles.Eleftherios Tachtsis - 2024 - Notre Dame Journal of Formal Logic 65 (3):311-331.
On the Deductive Strength of Various Distributivity Axioms for Boolean Algebras in Set Theory.Yasuo Kanai - 2002 - Mathematical Logic Quarterly 48 (3):413-426.
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