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 gemeinsammen Teiler." In Gesammelte Werke, Bd. 1. (Ed. K. May). Heidelberg, Germany: Mohr Siebeck, pp. 103-148, 1897.Jäkel, C. "A Computation of the Ninth Dedekind Number." 3 Apr 2023. https://arxiv.org/abs/2304.00895.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 Web Resource. https://mathworld.wolfram.com/DedekindsProblem.html