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arXiv · 1208.3796

The Causal Poset is Directed but not Lattice Ordered

Stanley P Gudder
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Abstract

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.

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Stanley P Gudder. 2012-08-19. The Causal Poset is Directed but not Lattice Ordered. https://arxiv.org/abs/1208.3796

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