A partially ordered set with a least element 0 has the disjunction property of Wallman if for every pair of elements of the poset, either or there exists an element such that and has no nontrivial common predecessor with . That is, in the latter case, the only with and is .

For the case if the poset is a -semilattice disjunction property of Wallman is equivalent to every of the following three formulas:

1. ;
2. ;
3. .

The proof of this equivalence can be found in this online article.