Submission date: 10 August 2023

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.

Mathematics Subject Classification: Primary 03C45, Secondary 37BXX, 54H15

Keywords and phrases:

Full text arXiv 2308.05477: pdf, ps.