We develop a notion of causal order on a generic manifold as independent of the underlying differential and topological structure. We show that sufficiently regular causal orders can be recovered from a distinguished algebra of sets, which plays a role analogous to that of topologies and $\sigma$ algebras. We then discuss how a natural notion of measure can be associated to the algebra of causal sets.

中文翻译：

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独立于背景的因果关系概念

我们在通用流形上发展了一种独立于底层微分和拓扑结构的因果顺序概念。我们证明，可以从一个杰出的集合代数中恢复足够规则的因果顺序，它的作用类似于拓扑和$\sigma$代数。然后我们讨论如何将自然的测量概念与因果集的代数联系起来。