Reichenbachian common cause systems

International Journal of Theoretical Physics 43:1819-1826 (2004)
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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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Author Profiles

Miklós Rédei
London School of Economics
Gábor Hofer-Szabó
Research Center For The Humanities, Budapest

Citations of this work

Minimal Assumption Derivation of a Bell-Type Inequality.Gerd Graßhoff, Samuel Portmann & Adrian Wüthrich - 2005 - British Journal for the Philosophy of Science 56 (4):663 - 680.
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Demarcating presentism.Christian Wuthrich - 2011 - In Henk W. De Regt, Stephan Hartmann & Samir Okasha, EPSA Philosophy of Science: Amsterdam 2009. Springer. pp. 441--450.

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