A generalized manifold topology for branching space-times

The logical theory of branching space-times (Belnap, Synthese 1992), which provides a relativistic framework for studying objective indeterminism, remains mostly disconnected from the discussion of space-time theories in the philosophy of physics. Earman has criticized the branching approach and suggested “pruning some branches from branching space-time” (2008). This paper identifies the different—order-theoretic vs. topological— points of view of both discussions as a reason for certain misunderstandings, and tries to remove them. Most importantly, we give a novel, topological criterion of modal consistency that usefully generalizes an earlier criterion, and we introduce a differentialgeometrical version of branching space-times as a non-Hausdorff (generalized) manifold.