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The number of nonisomorphic Boolean subalgebras of a power set


Author: Francisco J. Freniche
Journal: Proc. Amer. Math. Soc. 91 (1984), 199-201
MSC: Primary 06E05; Secondary 03G05
MathSciNet review: 740170
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Abstract: It is shown that if $ \kappa $ is an infinite cardinal, then there are $ {2^{{2^\kappa }}}$ nonisomorphic Boolean subalgebras of $ \mathcal{P}\left( \kappa \right)$. Also it is shown that if $ \kappa = c$, then the above subalgebras can be choosen countably complete. This solves a question raised by S. Ulam.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0740170-X
Keywords: Boolean algebra, almost disjoint family, large oscillation family
Article copyright: © Copyright 1984 American Mathematical Society