A Model in Which Every Boolean Algebra Has Many Subalgebras

Abstract

We show that it is consistent with ZFC (relative to large cardinals) that every infinite Boolean algebra B has an irredundant subsetA 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… (More)

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