Abstract
Let \(\langle {\mathcal{D}}, \leq \rangle\) be the ordered set of isomorphism types of finite distributive lattices, where the ordering is by embeddability. We characterize the order ideals in \(\langle {\mathcal{D}}, \leq \rangle\) that are well-quasi-ordered by embeddability, and thus characterize the members of \(\mathcal{D}\) that belong to at least one infinite anti-chain in \(\mathcal{D}\).
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