Definition
A causal set (or causet) is a set with a partial order relation that is
- Reflexive: For all, we have .
- Antisymmetric: For all, we have .
- Transitive: For all, we have implies .
- Locally finite: For all, we have card.
Here card denotes the cardinality of a set . We'll write if and .
The set represents the set of spacetime events and the order relation represents the causal relationship between events (see causal structure for the analogous idea in a Lorentzian manifold).
Although this definition uses the reflexive convention we could have chosen the irreflexive convention in which the order relation is irreflexive. The causal relation of a Lorentzian manifold (without closed causal curves) satisfies the first three conditions. It is the local finiteness condition that introduces spacetime discreteness.
Read more about this topic: Causal Sets
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