Reichenbachian Common Cause Systems of Arbitrary Finite Size Exist |
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Authors: | Gábor Hofer-Szabó Miklós Rédei |
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Institution: | 1. Department of Philosophy and History of Science, Budapest University of Technology Economics, Budapest, Hungary 2. Department of History and Philosophy of Science, E?tv?s University, Budapest, Hungary
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Abstract: | A partition 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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Keywords: | probability measure space correlation Reichenbachian common cause |
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