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### Subposets of the Boolean lattice via Sage

Let $B_n$ be the Boolean lattice of a set with $n$ elements. Is there a quick method via Sage to obtain all subposets $P$ of $B_n$ containing the empty set and having the property that with x in $P$ also the complement of the set x is in P and such that with x and y in P also the union of x and y is in P if x and y are disjoint?

Thanks for any help

### Subposets of the Boolean lattice via Sage

Let $B_n$ be the Boolean lattice of a set with $n$ elements. Is there a quick method via Sage to obtain all subposets $P$ of $B_n$ containing the empty set and having the property that with x in $P$ also the complement of the set x is in P and such that with x and y in P also the union of x and y is in P if x and y are disjoint?

disjoint? (probably this works only for small $n$ but $n \leq 6$ would already be interesting) Thanks for any help