The Causal Poset Is Directed but Not Lattice Ordered
Causal set approach, Discrete quantum gravity, Quantum sequential growth process
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