Garcia, Octavio; Nelson, Evelyn On the nonexistence of free complete distributive lattices. (English) Zbl 0558.06012 Order 1, 399-403 (1985). 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 Cited in 6 Documents MSC: 06D05 Structure and representation theory of distributive lattices 06D10 Complete distributivity Keywords:countably generated lattices of large cardinality; complete distributive lattices PDFBibTeX XMLCite \textit{O. Garcia} and \textit{E. Nelson}, Order 1, 399--403 (1985; Zbl 0558.06012) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.