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, Volume 1, Issue 4, pp 399–403 | Cite as

On the nonexistence of free complete distributive lattices

  • Octavio Garcia
  • Evelyn Nelson
Article

Abstract

We prove that there is no free object over a countable set in the category of complete distributive lattices with homomorphisms preserving binary meets and arbitrary joins.

AMS (MOS) subject classifications (1980)

06A23 06D05 08B20 

Key words

Complete distributive lattices free objects 

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References

  1. 1.
    P. Crawley and R. A. Dean (1959) Free lattices and infinite operations,Trans. Amer. Math. Soc. 92, 35–47.Google Scholar
  2. 2.
    H. Gaifman (1964) Infinite Boolean polynomials I,Fund. Math. 54, 229–250.Google Scholar
  3. 3.
    A. W. Hales (1964) On the nonexistence of free complete Boolean algebras,Fund. Math. 54, 45–66.Google Scholar
  4. 4.
    Robert Solovay (1966) A new proof of a theorem of Gaifman and Hales,Bull. Amer. Math. Soc. 72, 282–284.Google Scholar

Copyright information

© D. Reidel Publishing Company 1985

Authors and Affiliations

  • Octavio Garcia
    • 1
  • Evelyn Nelson
    • 2
  1. 1.Instituto de MatematicasUNAMMexico
  2. 2.Department of Mathematical SciencesMcMaster UniversityHamiltonCanada

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