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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Not all $ \sigma$-complete Boolean algebras are quotients of complete Boolean algebras


Authors: A. Dow and J. Vermeer
Journal: Proc. Amer. Math. Soc. 116 (1992), 1175-1177
MSC: Primary 54G05; Secondary 03G05, 06E10, 54A35, 54G20
MathSciNet review: 1137221
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Abstract: In Shelah's model of no Borel lifting of the measure algebra we show that there is a $ \sigma $-complete Boolean algebra of cardinality $ {2^\omega }$ that is not a quotient of a complete Boolean algebra. By Stone duality, there is a basically disconnected space of weight $ {2^\omega }$ that cannot be embedded into an extremally disconnected space.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1137221-4
PII: S 0002-9939(1992)1137221-4
Keywords: $ (\sigma-)$complete Boolean algebra, extremally disconnected, basically disconnected
Article copyright: © Copyright 1992 American Mathematical Society



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