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 wordsComplete distributive lattices free objects
Unable to display preview. Download preview PDF.
- 1.P. Crawley and R. A. Dean (1959) Free lattices and infinite operations,Trans. Amer. Math. Soc. 92, 35–47.Google Scholar
- 2.H. Gaifman (1964) Infinite Boolean polynomials I,Fund. Math. 54, 229–250.Google Scholar
- 3.A. W. Hales (1964) On the nonexistence of free complete Boolean algebras,Fund. Math. 54, 45–66.Google Scholar
- 4.Robert Solovay (1966) A new proof of a theorem of Gaifman and Hales,Bull. Amer. Math. Soc. 72, 282–284.Google Scholar
© D. Reidel Publishing Company 1985