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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Irredundant sets in Boolean algebras


Author: Stevo Todorčević
Journal: Trans. Amer. Math. Soc. 339 (1993), 35-44
MSC: Primary 03E50; Secondary 06E05
DOI: https://doi.org/10.1090/S0002-9947-1993-1080736-3
MathSciNet review: 1080736
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Abstract: It is shown that every uncountable Boolean algebra $ A$ contains an uncountable subset $ I$ such that no $ a$ of $ I$ is in the subalgebra generated by $ I\backslash \{ a\} $ using an additional axiom of set theory. It is also shown that a use of some such axiom is necessary.


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DOI: https://doi.org/10.1090/S0002-9947-1993-1080736-3
Article copyright: © Copyright 1993 American Mathematical Society