Free Completely Distributive Lattices
We show that the usual construction of the free distributive lattice on n generators generalizes to an arbitrary quantity of generators and actually yields a free completely distributive lattice. Furthermore, for an infinite number of generators the cardinality of the corresponding free completely distributive lattice is exactly that of the power set of the power set of the set of generators.
G. Markowsky, "Free Completely Distributive Lattices," Proceedings of the American Mathematical Society, vol. 74, no. 2, pp. 227-228, American Mathematical Society, May 1979.
The definitive version is available at https://doi.org/10.1090/S0002-9939-1979-0524290-9
Keywords and Phrases
Free completely distributive lattice; Free distributive lattice
International Standard Serial Number (ISSN)
Article - Journal
© 1979 American Mathematical Society, All rights reserved.