Definability in substructure orderings, I: finite semilattices

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• 作者：Jaroslav Je?ek and Ralph McKenzie
• 关键词：definable ; semilattice ; lattice
• 刊名：Algebra Universalis
• 出版年：2009
• 出版时间：October, 2009
• 年：2009
• 卷：61
• 期：1
• 页码：59-75
• 全文大小：250.1 KB

文摘

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.