TY - JOUR AB - We offer further evidence that discreteness of the sort inherent in a causal set cannot, in and of itself, serve to break Poincaré invariance. In particular we prove that a Poisson sprinkling of Minkowski spacetime cannot endow spacetime with a distinguished spatial or temporal orientation, or with a distinguished lattice of spacetime points, or with a distinguished lattice of timelike directions (corresponding respectively to breakings of reflection-invariance, translation-invariance, and Lorentz invariance). Along the way we provide a proof from first principles of the zero-one law on which our new arguments are based. AU - Dowker,F AU - Sorkin,RD DO - 1361-6382/ab81cd PY - 2020/// SN - 0264-9381 TI - Symmetry-breaking and zero-one laws T2 - Classical and Quantum Gravity UR - http://dx.doi.org/10.1088/1361-6382/ab81cd UR - https://iopscience.iop.org/article/10.1088/1361-6382/ab81cd UR - http://hdl.handle.net/10044/1/77788 VL - 37 ER -