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arXiv · 2308.05477

Ranks in Ellis semigroups and model theory

Alessandro Codenotti·Daniel Max Hoffmann
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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.

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Alessandro Codenotti, Daniel Max Hoffmann. 2023-08-10. Ranks in Ellis semigroups and model theory. https://arxiv.org/abs/2308.05477

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