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Order

, Volume 7, Issue 1, pp 97–99 | Cite as

The order dimension of relatively free lattices

  • J. B. Nation
  • J. H. Schmerl
Article

Abstract

If V is a nontrivial lattice variety and λ is an infinite cardinal, then the order dimension of FV(λ) is the smallest cardinal κ such that λ≤2κ.

AMS subject classification (1980)

06B25 

Key words

Order dimension free lattice 

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References

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    B.Balcar and F.Franěk (1982) Independent families in complete Boolean Algebras, Trans. Amer. Math. Soc. 274, 607–618.Google Scholar
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    R.Freese and J. B.Nation (1987) Projective lattices, Pacific J. Math. 75, 93–106.Google Scholar
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    F.Hausdorff (1936) Über zwei Sätze von G. Fichtenholt und L. Kantorovitch, Studia Math. 6, 18–19.Google Scholar
  4. 4.
    J. B.Nation (1984) On partially ordered sets embeddable in a free lattice, Algebra Universalis 18, 327–333.Google Scholar
  5. 5.
    E.Szpilrajn (1930) Sur l'extension de l'ordre partiel, Fund. Math. 16, 386–389.Google Scholar

Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • J. B. Nation
    • 1
  • J. H. Schmerl
    • 2
  1. 1.Department of MathematicsUniversity of HawaiiHonoluluUSA
  2. 2.Department of MathematicsUniversity of ConnecticutStorrsUSA

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