The Causal Poset is Directed but not Lattice Ordered
Causal set approach, discrete quantum gravity
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.
Gudder, S. (2012). The causal poset is directed but not lattice ordered. Mathematics Preprint Series. Retrieved from https://digitalcommons.du.edu/math_preprints/28