Definability in substructure orderings, I: finite semilattices
نویسندگان
چکیده
We investigate definability in the set of isomorphism types of finite semilattices ordered by embeddability; we prove, among other things, that every finite semilattice is a definable element in this ordered set. Then we apply these results to investigate definability in the closely related lattice of universal classes of semilattices; we prove that the lattice has no non-identical automorphisms, the set of finitely generated and also the set of finitely axiomatizable universal classes are definable subsets and each element of the two subsets is a definable element in the lattice.
منابع مشابه
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...
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