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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Free completely distributive lattices


Author: George Markowsky
Journal: Proc. Amer. Math. Soc. 74 (1979), 227-228
MSC: Primary 06D05
DOI: https://doi.org/10.1090/S0002-9939-1979-0524290-9
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