Model theory of probability spaces with an automorphism
Logic
2007-05-23 v1 Dynamical Systems
Abstract
The class of generic structures among those consisting of the measure algebra of a probability space equipped with an automorphism is axiomatizable by positive sentences interpreted using an approximate semantics. The separable generic structures of this kind are exactly the ones isomorphic to the measure algebra of a standard Lebesgue space equipped with an aperiodic measure-preserving automorphism. The corresponding theory is complete and has quantifier elimination; moreover it is stable with built-in canonical bases. We give an intrinsic characterization of its independence relation.
Cite
@article{arxiv.math/0405360,
title = {Model theory of probability spaces with an automorphism},
author = {Alexander Berenstein and C. Ward Henson},
journal= {arXiv preprint arXiv:math/0405360},
year = {2007}
}
Comments
31 pages