  How is the boundary-value problem changed by this alteration in the space-time? Before the cut and paste, we can put arbitrary data on the simultaneity slice S and continue it to a unique solution. After the change in topology, S is no longer a Cauchy surface, since a CTC will never intersect it, but it is a partial Cauchy surface. So we can ask two questions. First, can arbitrary data on S always be continued to a global solution? Second, is that solution unique? If the answer to the first question is no, then we have a backward-temporal constraint: the existence of the region with CTCs places constraints on what can happen on S even though that region lies completely to the future of S. If the answer to the second question is no, then we have an odd sort of indeterminism: the complete physical state on S does not determine the physical state in the future, even though the local dynamics is perfectly deterministic and even though there is no other past edge to the space-time region in S's future (i.e., there is nowhere else for boundary values to come from which could influence the state of the region).