The Boolean lattice B(n) is the partial order of all subsets of {0,…,n−1}, ordered by inclusion. It forms a Hasse diagram where each node is a subset, edges connect sets differing by one element, and rank (height) equals set cardinality. By Dilworth's theorem, the maximum antichain has size C(n, ⌊n/2⌋) — the Sperner's theorem result (1928). The lattice is also the n-dimensional hypercube graph, connecting nodes that differ in exactly one bit. Highlighted nodes show join-closed upsets — filters in lattice theory, corresponding to monotone Boolean functions.