Publication

Proceedings of the American Mathematical Society

Paper

# Free completely distributive lattices

## Abstract

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. © 1979 American Mathematical Society.