Universal homogeneous causal sets

Abstract

Causal sets are particular partially ordered sets which have been proposed as a basic model for discrete space-time in quantum gravity. We show that the class C of all countable past-finite causal sets contains a unique causal set (U,<) which is universal (i.e., any member of C can be embedded into (U,<)) and homogeneous (i.e., (U,<) has maximal degree of symmetry). Moreover, (U,<) can be constructed both probabilistically and explicitly. In contrast, the larger class of all countable causal sets does not contain a universal object.

14 pages

References in corpus (3)

• "Observables" in causal set cosmology
• General Covariance and the "Problem of Time" in a Discrete Cosmology
• Moment Problems and the Causal Set Approach to Quantum Gravity

Cited by in corpus (2)

• Foliations and automorphisms of causal sets
• Bifinite Chu Spaces