Ranks in Ellis semigroups and model theory
Logic
2023-09-07 v2 Dynamical Systems
Abstract
We slightly generalize a notion of rank introduced by Glasner and Megrelishvili, which captures the oscillations of elements of Ellis semigroups, so that it can be applied to any compact Hausdorff space instead of being limited to the metric case. Then, we relate this rank to classical dividing lines in the model-theoretic stability hierarchy. For example, that the rank is ordinal-valued if and only if the background theory is NIP.
Keywords
Cite
@article{arxiv.2308.05477,
title = {Ranks in Ellis semigroups and model theory},
author = {Alessandro Codenotti and Daniel Max Hoffmann},
journal= {arXiv preprint arXiv:2308.05477},
year = {2023}
}