AXIOMS FOR THE THEORY OF RANDOM VARIABLE STRUCTURES: AN ELEMENTARY APPROACH

- Journal title : Journal of the Korean Mathematical Society
- Volume 51, Issue 3, 2014, pp.527-543
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2014.51.3.527

Title & Authors

AXIOMS FOR THE THEORY OF RANDOM VARIABLE STRUCTURES: AN ELEMENTARY APPROACH

Song, Shichang;

Song, Shichang;

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.

Keywords

continuous logic;axiomatization;random variable;

Language

English

Cited by

References

1.

I.Ben Yaacov, Modular functionals and perturbations of Nakano spaces, J. Log. Anal., 1:1 (2009), 1-42.

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.

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.