Abstract
A partition \(\{C_i\}_{i\in I}\) of a Boolean algebra Ω in a probability measure space (Ω, p) is called a Reichenbachian common cause system for the correlation between a pair A,B of events in Ω 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 non-strict correlation in (Ω, p), and given any finite natural number n > 2, the probability space (Ω,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.
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Hofer-Szabó, G., Rédei, M. Reichenbachian Common Cause Systems of Arbitrary Finite Size Exist. Found Phys 36, 745–756 (2006). https://doi.org/10.1007/s10701-005-9040-x
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DOI: https://doi.org/10.1007/s10701-005-9040-x