Definability in substructure orderings, IV: finite lattices

Let L be the ordered set of isomorphism types of finite lattices, where the ordering is by embeddability. We study first-order definability in this ordered set. Our main result is that for every finite lattice L, the set {l, l} is definable, where l and l are the isomorphism types of L and its opposite (L turned upside down). We shall show that the only non-identity automorphism of L is the map l 7→ l.