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Consider the following curious puzzle: call an n-tuple X=(X_1, ..., X_n) ofsets smaller than another n-tuple Y if it has fewer //unordered sections//. Weshow that equivalence classes for this preorder are very easy to describe andcharacterize the preorder in terms of the simpler pointwise inclusion and theexistence of a special increasing boolean operator f:B^n -> B^n. We also showthat contrary to increasing boolean operators, the relevant operators are notfinitely generated, which might explain why this preorder is not easy todescribe concretely.

Some Properties of Inclusions of Multisets and Contractive Boolean Operators