Abstract:Let F be a partially ordered set (poset). A poset P is called F-free if P contains no subposet isomorphic to F. A finite poset F is said to have the maximal element property if every maximal F-free subposet of any finite poset P contains a maximal element of P. It is shown that a poset F with at least two elements has the maximal element property if and only if F is an antichain or F ∼ = 2 + 2.
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