Not all $\sigma$-complete Boolean algebras are quotients of complete Boolean algebras
نویسندگان
چکیده
منابع مشابه
Complete Ccc Boolean Algebras
Let B be a complete ccc Boolean algebra and let τs be the topology on B induced by the algebraic convergence of sequences in B. 1. Either there exists a Maharam submeasure on B or every nonempty open set in (B, τs) is topologically dense. 2. It is consistent that every weakly distributive complete ccc Boolean algebra carries a strictly positive Maharam submeasure. 3. The topological space (B, τ...
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It is a well-known theorem of R. S. Pierce that, for every infinite cardinal a, a 0 = a if and only if there is a complete Boolean algebra B s.t. card B = a (see [3, Theorem 25.4]). Recently, Comfort and Hager proved [l] that, for every infinite a-complete Boolean algebra B, (card B) 0 _ card B. We extend this result to the class of homomorphic images of cr-complete algebras, following closely ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1992
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1992-1137221-4