Free completely distributive lattices

Author:
George Markowsky

Journal:
Proc. Amer. Math. Soc. **74** (1979), 227-228

MSC:
Primary 06D05

MathSciNet review:
524290

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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.

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DOI:
https://doi.org/10.1090/S0002-9939-1979-0524290-9

Keywords:
Free distributive lattice,
free completely distributive lattice

Article copyright:
© Copyright 1979
American Mathematical Society