all four-simplices in a given slab is consistent with this notion of time. In this way the causal structure becomes linked to a preferred discrete foliation of spacetime.

To understand better how the preferred time foliation on the one hand and the causal structure on the other contribute to the evidence of a good classical limit – the key distinguishing feature of CDT quantum gravity – it would be highly desirable to disentangle these two elements of “background structure". We recently proposed a modification of standard CDT which does exactly that [@jl]. The main idea, applicable in any spacetime dimension $d$, is to enlarge the set of $d$-simplices by new types of simplicial building blocks, also pieces of $d$-dimensional Minkowski space, but with different link type assignments and therefore a different orientation of the light cone relative to the boundaries of the simplex. Including the new building blocks is in general not compatible with the preferred foliation of CDT. Nevertheless, with a suitable choice of gluing rules one can still obtain Lorentzian simplicial manifolds with a well-defined causal structure, at least locally. In this way the issue of causality becomes dissociated from the notion of a preferred foliation. The interesting 