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On the nonexistence of free complete distributive lattices. (English) Zbl 0558.06012

It is shown that there are complete distributive lattices of arbitrarily large cardinality generated by a countable set under finite joins and arbitrary meets.
Reviewer: Ch.Herrmann

MSC:

06D05 Structure and representation theory of distributive lattices
06D10 Complete distributivity
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References:

[1] P. Crawley and R. A. Dean (1959) Free lattices and infinite operations,Trans. Amer. Math. Soc. 92, 35-47. · Zbl 0115.02002 · doi:10.1090/S0002-9947-1959-0108447-9
[2] H. Gaifman (1964) Infinite Boolean polynomials I,Fund. Math. 54, 229-250. · Zbl 0126.26404
[3] A. W. Hales (1964) On the nonexistence of free complete Boolean algebras,Fund. Math. 54, 45-66. · Zbl 0119.26003
[4] Robert Solovay (1966) A new proof of a theorem of Gaifman and Hales,Bull. Amer. Math. Soc. 72, 282-284. · Zbl 0158.24903 · doi:10.1090/S0002-9904-1966-11493-3
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