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Transactions of the American Mathematical Society

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Independent families in complete Boolean algebras


Authors: B. Balcar and F. Franěk
Journal: Trans. Amer. Math. Soc. 274 (1982), 607-618
MSC: Primary 06E10; Secondary 03G05, 04A20, 54A20, 54G05
MathSciNet review: 675069
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Abstract: We present a proof (without any set-theoretical assumptions) that every infinite complete Boolean algebra includes a free subalgebra of the same cardinality. It follows that the set of all ultrafilters on an infinite complete Boolean algebra $ B$ has power $ 2^{\vert B\vert}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0675069-3
Article copyright: © Copyright 1982 American Mathematical Society