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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… (More)

Let B, C be Boolean algebras and e : B → C an embedding. We examine the hierarchy of ideals on C for which e : B → C/I is a regular (i.e. complete) embedding. As an application we deal with the interrelationship between P(ω)/fin in the ground model and in its extension. If M is an extension of V containing a new subset of ω, then in M there is an almost… (More)

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