P(ω)/fin contains a family {B_X : X ⊆ c} of subalgebras such that X ⊆ Y implies B_Y ⊆ B_X and otherwise B_Y does not embed into B_X, constructed via Stone duality on a family of separable zero-dimensional compact spaces.
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Many subalgebras of $\mathcal{P}(\omega)/\mathit{fin}$
P(ω)/fin contains a family {B_X : X ⊆ c} of subalgebras such that X ⊆ Y implies B_Y ⊆ B_X and otherwise B_Y does not embed into B_X, constructed via Stone duality on a family of separable zero-dimensional compact spaces.