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Let P be a finite poset.

Is there an easy way to obtain the poset U(P) of intervals of P up to isomorphism?

So the elements of U(P) are the intervals of P up to isomorphism and x<=y in U(P) if x is isomorphic to a subposet of y.

For example if P is the lattice of divisors of the number 12, then U(P) contains 5 elements. Namely the poset with 1 element, the chain with 2 elements, the chain with 3 elements, the Boolean lattice of a 2-set and the poset P itself. U(P) is isomorphic to the Boolean lattice of a 2-set with a minimum appended.

Let P be a finite poset.

Is there an easy way to obtain the poset U(P) of intervals of P up to isomorphism?

So the elements of U(P) are the intervals of P up to isomorphism and x<=y in U(P) if x is isomorphic to a subposet an interval of y.

For example if P is the lattice of divisors of the number 12, then U(P) contains 5 elements. Namely the poset with 1 element, the chain with 2 elements, the chain with 3 elements, the Boolean lattice of a 2-set and the poset P itself. U(P) is isomorphic to the Boolean lattice of a 2-set with a minimum appended.