Branching space-times, general relativity, the Hausdorff property, and modal consistency

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Muller, Thomas
preprint description
The logical theory of branching space-times (BST; Belnap, Synthese 1992), which is intended to provide a framework for studying objective indeterminism, remains at a certain distance from the discussion of space-time theories in the philosophy of physics. In a welcome attempt to clarify the connection, Earman has recently found fault with the branching approach and suggested ``pruning some branches from branching space-time'' (2008). The present note identifies the different---order theoretic vs. topological---points of view of both discussion 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 the order-theoretic criterion of directedness, and we introduce a differential-geometrical version of BST based on the theory of non-Hausdorff (generalized) manifolds.