On the Computability of the Ninth Dedekind Number

The Dedekind numbers are an integer sequence that describes the number of n-variable monotone Boolean functions. It is reducible to counting other distinguished mathematical notions: antichains of subsets of n-set and simplicial complexes on an n-vertex set. The terms for $0 \le n\le 8$ are known and $n=9$ has been an open problem for over three decades. In this paper, we discuss the computability of the ninth Dedekind number with recent results involving partially ordered sets by Berman and Kohler [1] and combinatorial approaches with other relevant sequences