A model in which every Boolean algebra has many subalgebras

Journal of Symbolic Logic 60 (3):992-1004 (1995)
Abstract
We show that it is consistent with ZFC (relative to large cardinals) that every infinite Boolean algebra B has an irredundant subset A such that 2 |A| = 2 |B| . This implies in particular that B has 2 |B| subalgebras. We also discuss some more general problems about subalgebras and free subsets of an algebra. The result on the number of subalgebras in a Boolean algebra solves a question of Monk from [6]. The paper is intended to be accessible as far as possible to a general audience, in particular we have confined the more technical material to a "black box" at the end. The proof involves a variation on Foreman and Woodin's model in which GCH fails everywhere
Keywords Boolean algebras   free subsets   Radin forcing
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DOI 10.2307/2275769
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Adding Closed Cofinal Sequences to Large Cardinals.Lon Berk Radin - 1982 - Annals of Mathematical Logic 22 (3):243-261.

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