, Volume 32, Issue 2, pp 239–243 | Cite as

Countable Homogeneous Lattices

  • A. Abogatma
  • J. K. Truss


We show that there are uncountably many countable homogeneous lattices. We give a discussion of which such lattices can be modular or distributive. The method applies to show that certain other classes of structures also have uncountably many homogeneous members.


Lattice Homogeneous Amalgamation property 

Mathematics Subject Classifications (2010)

06A99 03G10 


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  1. 1.
    Bergman, G.: Coproducts and some universal ring constructions. Trans. Am. Math. Soc. 200, 33–87 (1974)MATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Bergman, G.: On coproducts in varieties, quasivarieties and prevarieties. Algebra Number Theory 3, 847–880 (2009)MATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Day, A., Ježek, J.: The amalgamation property for varieties of lattices. Trans. Am. Math. Soc. 286, 251–256 (1984)MATHCrossRefGoogle Scholar
  4. 4.
    Dilworth, R. P.: Lattices with unique complements. Trans. Am. Math. Soc. 57, 123–154 (1945)MATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Grätzer, G.: General Lattice Theory. Birkhäuser Verlag, Basel (1978)CrossRefGoogle Scholar
  6. 6.
    Grätzer, G., Jónsson, B., Lakser, H.: The amalgamation property in equational classes of modular lattices. Pac. J. Math. 45, 507–524 (1973)MATHCrossRefGoogle Scholar
  7. 7.
    Hodges, W.: A Shorter Model Theory. Cambridge University Press (1997)Google Scholar
  8. 8.
    Jónsson, B.: Universal relational systems. Math. Scand. 4, 193–208 (1956)MATHMathSciNetGoogle Scholar
  9. 9.
    Lachlan, A. H., Woodrow, R.: Countable ultrahomogeneous undirected graphs. Trans. Am. Math. Soc. 262, 51–94 (1980)MATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    Pierce, R. S.: Introduction to the Theory of Abstract Algebras. Holt, Rinehart and Winston, New York (1968)Google Scholar
  11. 11.
    Schmerl, J. H.: Countable homogeneous partially ordered sets. Algebra Univers. 9, 317–321 (1979)MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of LeedsLeedsUK
  2. 2.Department of MathematicsUniversity of Garyounis BenghaziBenghaziLibya

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