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Definability in substructure orderings, I: finite semilattices

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Abstract

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.

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References

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Authors and Affiliations

  1. Department of Mathematics, Charles University, Prague, Czech Republic

    Jaroslav Ježek

  2. Department of Mathematics, Vanderbilt University, Nashville, TN, 37235, USA

    Ralph McKenzie

Authors
  1. Jaroslav Ježek
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  2. Ralph McKenzie
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Correspondence to Jaroslav Ježek.

Additional information

Presented by M. Valeriote.

While working on this paper, the first author (Ježek) and the second author (McKenzie) were supported by US NSF grant DMS-0604065. The first author was also supported by the institutional grant MSM0021620839 financed by MSMT and partially supported by the grant GAČR 201/05/0002.

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Ježek, J., McKenzie, R. Definability in substructure orderings, I: finite semilattices. Algebra Univers. 61, 59 (2009). https://doi.org/10.1007/s00012-009-0002-6

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  • DOI: https://doi.org/10.1007/s00012-009-0002-6

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