Independent families in complete Boolean algebras

Balcar, B.; Franěk, F.

doi:10.1090/S0002-9947-1982-0675069-3

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
DOI: https://doi.org/10.1090/S0002-9947-1982-0675069-3
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 has power $2^{\vert B\vert}$ .

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