Free completely distributive lattices
HTML articles powered by AMS MathViewer
- by George Markowsky PDF
- Proc. Amer. Math. Soc. 74 (1979), 227-228 Request permission
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.References
- Garrett Birkhoff, Lattice theory, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1967. MR 0227053
- H. Gaifman, Infinite Boolean polynomials. I, Fund. Math. 54 (1964), 229–250. MR 168503, DOI 10.4064/fm-54-3-229-250
- A. W. Hales, On the non-existence of free complete Boolean algebras, Fund. Math. 54 (1964), 45–66. MR 163863, DOI 10.4064/fm-54-1-45-66
- D. Kleitman and G. Markowsky, On Dedekind’s problem: the number of isotone Boolean functions. II, Trans. Amer. Math. Soc. 213 (1975), 373–390. MR 382107, DOI 10.1090/S0002-9947-1975-0382107-0
- A. D. Koršunov, Solution of Dedekind’s problem on the number of monotone Boolean functions, Dokl. Akad. Nauk SSSR 233 (1977), no. 4, 543–546 (Russian). MR 0690078 G. Markowsky, Combinatorial aspects of lattice theory with applications to the enumeration of free distributive lattices, Ph.D. Thesis, Harvard University, 1973.
- A. Nerode, Composita, equations, and freely generated algebras, Trans. Amer. Math. Soc. 91 (1959), 139–151. MR 104609, DOI 10.1090/S0002-9947-1959-0104609-5
Additional Information
- © Copyright 1979 American Mathematical Society
- 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