Model theoretic properties of dynamics on the Cantor set
Logic
2021-03-25 v1 Dynamical Systems
Abstract
We examine topological dynamical systems on the Cantor set from the point of view of the continuous model theory of commutative C*-algebras. After some general remarks we focus our attention on the generic homeomorphism of the Cantor set, as constructed by Akin, Glasner, and Weiss. We show that this homeomorphism is the prime model of its theory. We also show that the notion of "generic" used by Akin, Glasner, and Weiss is distinct from the notion of "generic" encountered in Fraisse theory.
Cite
@article{arxiv.2103.12880,
title = {Model theoretic properties of dynamics on the Cantor set},
author = {Christopher J. Eagle and Alan Getz},
journal= {arXiv preprint arXiv:2103.12880},
year = {2021}
}
Comments
14 pages