The determination of the number of monotone Boolean functions of 
variables (equivalent to the number of antichains on
the 
-set
) is called Dedekind's problem,
and the numbers themselves are known as Dedekind numbers.
Dedekind's Problem
See also
Antichain, Boolean Function, Dedekind NumberExplore with Wolfram|Alpha
References
Dedekind, R. "Über Zerlegungen von Zahlen durch ihre grössten gemeinsamen Theiler." In Festschrift der Technischen Hochschule zu Braunschweig bei Gelegenheit der 69. Versammlung Deutscher Naturforscher und Ärzte. Braunschweig, Germany: Meyer, pp. 1-40, 1897. https://doi.org/10.1007/978-3-663-07224-9_1. Reprinted in Gesammelte mathematische Werke, Bd. 2 (Ed. R. Fricke, E. Noether, and Ø. Ore). Braunschweig, Germany: Vieweg, pp. 103-147, 1931. https://gdz.sub.uni-goettingen.de/id/PPN235693928.Jäkel, C. "A Computation of the Ninth Dedekind Number." J. Comput. Algebra 6-7, 100006, 2023. https://doi.org/10.1016/j.jaca.2023.100006.Kleitman, D. "On Dedekind's Problem: The Number of Monotone Boolean Functions." Proc. Amer. Math. Soc. 21, 677-682, 1969.Kleitman, D. and Markowsky, G. "On Dedekind's Problem: The Number of Isotone Boolean Functions. II." Trans. Amer. Math. Soc. 213, 373-390, 1975.Referenced on Wolfram|Alpha
Dedekind's ProblemCite this as:
Weisstein, Eric W. "Dedekind's Problem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DedekindsProblem.html