Reichenbachian common cause systems

Abstract
A partition $\{C_i\}_{i\in I}$ of a Boolean algebra $\cS$ in a probability measure space $(\cS,p)$ is called a Reichenbachian common cause system for the correlated pair $A,B$ of events in $\cS$ if any two elements in the partition behave like a Reichenbachian common cause and its complement, the cardinality of the index set $I$ is called the size of the common cause system. It is shown that given any correlation in $(\cS,p)$, and given any finite size $n>2$, the probability space $(\cS,p)$ can be embedded into a larger probability space in such a manner that the larger space contains a Reichenbachian common cause system of size $n$ for the correlation. It also is shown that every totally ordered subset in the partially ordered set of all partitions of \cS$ contains only one Reichenbachian common cause system. Some open problems concerning Reichenbachian common cause systems are formulated.
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Bell Inequality and Common Causal Explanation in Algebraic Quantum Field Theory.Gábor Hofer-Szabó & Péter Vecsernyés - 2013 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 44 (4):404-416.
Realism and Objectivism in Quantum Mechanics.Vassilios Karakostas - 2012 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 43 (1):45-65.
Distinguishing Causality Principles.Miklós Rédei & Iñaki Pedro - 2012 - Studies in History and Philosophy of Science Part B 43 (2):84-89.

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