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J. Korean Math. Soc. 2014; 51(3): 527-543
Printed May 1, 2014
https://doi.org/10.4134/JKMS.2014.51.3.527
Copyright © The Korean Mathematical Society.
Axioms for the theory of random variable structures: an elementary approach
Shichang Song
Beijing Jiaotong University
The theory of random variable structures was first studied by Ben Yaacov in~\cite{RandVar}. Ben Yaacov's axiomatization of the theory of random variable structures used an early result on the completeness theorem for \L{}ukasiewicz's $[0,1]$-valued propositional logic. In this paper, we give an elementary approach to axiomatizing the theory of random variable structures. Only well-known results from probability theory are required here.
Keywords: continuous logic, axiomatization, random variable
MSC numbers: Primary 03C90, 03C98, 60A05
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