Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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AXIOMS FOR THE THEORY OF RANDOM VARIABLE STRUCTURES: AN ELEMENTARY APPROACH

  • Song, Shichang (Department of Mathematics Beijing Jiaotong University)
  • Received : 2013.09.15
  • Published : 2014.05.01
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Abstract

The theory of random variable structures was first studied by Ben Yaacov in [2]. Ben Yaacov's axiomatization of the theory of random 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.

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References

  1. I.Ben Yaacov, Modular functionals and perturbations of Nakano spaces, J. Log. Anal., 1:1 (2009), 1-42.
  2. I.Ben Yaacov, On theories of random variables, Israel J. Math., 194 (2013), 957-1012. https://doi.org/10.1007/s11856-012-0155-4
  3. I.Ben Yaacov, A.Berenstein, C.W.Henson, and A.Usvyatsov, Model theory for metric structures, in: Model Theory with Applications to Algebra and Analysis, Volume 2, (Zoe Chatzidakis, Dugald Macpherson, Anand Pillay and Alex Wilkie, eds.), London Math Society Lecture Note Series, No. 350, Cambridge University Press, 315-427, 2008.
  4. I.Ben Yaacov and A.Usvyatsov, Continuous first order logic and local stability, Trans. Amer. Math. Soc., 362 (2010), 5213-5259. https://doi.org/10.1090/S0002-9947-10-04837-3
  5. A.Berenstein and C.W.Henson, Model theory of probability spaces with an automor-phism, submitted.
  6. S. Song, Model theory and probability, PhD Thesis, University of Illinois at Urbana-Champaign, 2011.

Cited by

  1. SATURATED STRUCTURES FROM PROBABILITY THEORY vol.53, pp.2, 2016, https://doi.org/10.4134/JKMS.2016.53.2.315