Not all 𝜎-complete Boolean algebras are quotients of complete Boolean algebras

Dow, A.; Vermeer, J.

doi:10.1090/S0002-9939-1992-1137221-4

Not all $\sigma$-complete Boolean algebras are quotients of complete Boolean algebras
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by A. Dow and J. Vermeer PDF

Proc. Amer. Math. Soc. 116 (1992), 1175-1177 Request permission

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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