AXIOMS FOR THE THEORY OF RANDOM VARIABLE STRUCTURES: AN ELEMENTARY APPROACH
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The theory of random variable structures was first studied by Ben Yaacov in [2]. Ben Yaacov’s axiomatization of the theory of ran- dom variable structures used an early result on the completeness theorem for Lukasiewicz’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.
Abstract
The theory of random variable structures was first studied by Ben Yaacov in [2]. Ben Yaacov’s axiomatization of the theory of ran- dom variable structures used an early result on the completeness theorem for Lukasiewicz’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.
참고문헌 (6)
- I.Ben Yaacov, "Modular functionals and perturbations of Nakano spaces", J. Log. Anal., 1(1), pp.1~42 (2009)
- I.Ben Yaacov, "On theories of random variables", Israel J. Math., 194, pp.957~1012 (2013)
- I.Ben Yaacov, "Model Theory with Applications to Algebra and Analysis, Volume 2", pp.315~427 (2008), Cambridge University Press
- I.Ben Yaacov, "Continuous first order logic and local stability", Trans. Amer. Math. Soc., 362, pp.5213~5259 (2010)
- A. Berenstein, "Model theory of probability spaces with an automor-phism", submitted, ~
- S. Song, "Model theory and probability", PhD, pp.2011