The central message of this paper is that indeterminism in measurement events and experimenters' free choice are enough to explain violations of Bell-type inequalities. To discuss the issue, I develop algebraic branching models that permit a unified discussion of modal, spatiotemporal, and probabilistic features. Some realizations of these models are given by branching structures of Minkowski space-times to which states are assigned. I draw a distinction between correlations produced by events from one history and correlations brought about by events that do not belong to one history. I prove that any finite number of the first kind of correlations can always be explained by a common cause, whereas for some correlations of the second kind, a single local common cause cannot be posited. I argue that the non-existence of common cause local models of the Bell-Aspect experiment derive from indeterminism in measurement events.
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