  Contrary to its initial idea, Belnap's (1992) theory of Branching Space-Times
(BST) has models in which histories do not resemble relativistic space-times or
any other physical space-times. The aim of this paper is to define a certain
class of BST models, called "Minkowskian Branching Structures" (MBS), in which
histories are isomorphic to Minkowski space-time. By focusing on these models
rather than on general BST models, we hope that one may be able to improve on
earlier BST analyzes of physical phenomena. Also, introducing MBS' sets the
stage for recent discussions about whether or not `branching is a bad idea',
physically speaking.
