Definability in substructure orderings, IV: Finite lattices |
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Authors: | J Ježek R McKenzie |
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Institution: | 1. Charles University, MFF, Sokolovská 83, 18600, Praha 8, Czech Republic 2. Department of Mathematics, Vanderbilt University, Nashville, TN, 37235, USA
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Abstract: | Let ${\mathcal{L}}$ 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 {?, ? opp} is definable, where ? and ? opp are the isomorphism types of L and its opposite (L turned upside down). We shall show that the only non-identity automorphism of ${\mathcal{L}}$ is the map ${\ell \mapsto \ell^{\rm opp}}$ . |
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