**G. Hofer-Szabó, M. Rédei and L. E. Szabó**
*On Reichenbach's common cause
principle and Reichenbach's notion of common cause*

Published in

*The British Journal for the
Philosophy of Science*,
**50 **(1999), 377-399.

**Abstract**

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 Reichenbach's
definition. It is argued that these results very strongly restrict the
possible ways of disproving Reichenbach's Common Cause Principle.

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