On Reichenbach's common cause principle and Reichenbach's notion of common cause

It is shown that, given any finite set of pairs of random events in a Boolean algebra which are correlated with respect to a fixed probability measure on the algebra, the algebra can be extended in such a way that the extension contains events that can be regarded as common causes of the correlations in the sense of Reichenbach's definition of common cause. It is shown, further, that, given any quantum probability space and any set of commuting events in it which are correlated with respect to a fixed quantum state, the quantum probability space can be extended in such a way that the extension contains common causes of all the selected correlations, where common cause is again taken in the sense of Reichenbachs definition. It is argued that these results very strongly restrict the possible ways of disproving Reichenbach's Common Cause Principle.
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DOI 10.1093/bjps/50.3.377
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Jeremy Butterfield (2007). Stochastic Einstein Locality Revisited. British Journal for the Philosophy of Science 58 (4):805 - 867.
Iñaki San Pedro (2012). Causation, Measurement Relevance and No-Conspiracy in EPR. European Journal for Philosophy of Science 2 (1):137-156.
Michał Marczyk & Leszek Wroński (2015). Completion of the Causal Completability Problem. British Journal for the Philosophy of Science 66 (2):307-326.

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