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Are there $2^{\aleph_0}$ pairwise non-isomorphic Boolean algebrasalgebra structures on $\omega$?

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YCor
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Is there a collection of $2^{\aleph_0}$ pairwise non-isomorphic countable Boolean algebras?

Equivalently, are there $2^{\aleph_0}$ pairwise non-homeomorphic closed subsets in the Cantor space?

Is there a collection of $2^{\aleph_0}$ pairwise non-isomorphic countable Boolean algebras?

Is there a collection of $2^{\aleph_0}$ pairwise non-isomorphic countable Boolean algebras?

Equivalently, are there $2^{\aleph_0}$ pairwise non-homeomorphic closed subsets in the Cantor space?

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Is there a collection of $2^{\aleph_0}$ pairwise non-isomorphic countable Boolean algebras on $\omega$?

Is there a collection of $2^{\aleph_0}$ pairwise non-isomorphic Boolean algebras on $\omega$?

Is there a collection of $2^{\aleph_0}$ pairwise non-isomorphic countable Boolean algebras?

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