  In the causal set approach to discrete quantum gravity the universe grows one
element at a time in discrete steps. At each step the process has the form of a
causal set (causet) and the "completed" universe is given by a path through a
discretely growing chain of causets. The collection of causets forms a
partially ordered set (poset) in a natural way. We first show that this poset
is directed. We then give a counterexample which shows it is not lattice
ordered.
