On theories of random variables
Logic
2014-02-17 v3
Abstract
We study theories of spaces of random variables: first, we consider random variables with values in the interval , then with values in an arbitrary metric structure, generalising Keisler's randomisation of classical structures. We prove preservation and non-preservation results for model theoretic properties under this construction: i) The randomisation of a stable structure is stable. ii) The randomisation of a simple unstable structure is not simple. We also prove that in the randomised structure, every type is a Lascar type.
Cite
@article{arxiv.0901.1584,
title = {On theories of random variables},
author = {Itaï Ben Yaacov},
journal= {arXiv preprint arXiv:0901.1584},
year = {2014}
}