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. * We read earlier versions of this paper at the seminar 'Chaos and Quantum Information' held at the Jagiellonian

In this paper we give a positive answer to a problem posed by Hofer-Szabó and Rédei (Int.

We give a few results concerning the notions of causal completability and causal closedness of classical probability spaces

We investigate how Dutch Book considerations can be conducted in the context of two classes of nonclassical probability spaces used in philosophy of physics. In particular we show that a recent proposal by B. Feintzeig to find so called "generalized probability spaces" which would not be susceptible to a Dutch Book and would not possess a classical extension is doomed to fail. Noting that the particular notion of a nonclassical probability space used by Feintzeig is not the most common employed in philosophy of physics, and that his usage of the "classical" Dutch Book concept is not appropriate in "nonclassical" contexts, we then argue that if we switch to the more frequently used formalism and use the correct notion of a Dutch Book, then all probability spaces are not susceptible to a Dutch Book. We also settle a hypothesis regarding the existence of classical extensions of a class of generalized probability spaces.