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How can I construct a countably infinite Boolean algebra with $n$ atoms, for $n \in \mathbb{N}$?

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I think the periodic sequences form a (the) countable atomless Boolean algebra, but how does this help? – natural Feb 5 '13 at 16:29

Hint: every boolean algebra is isomorphic to an algebra of sets. What happens if you add together (and generate algebra with) two algebras of sets with disjoint universes?

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