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arXiv · 2609.25132

Ramsey theory and topological dynamics of 0-dimensional flows

Krzysztof Krupiński·Junguk Lee·Slavko Moconja
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Abstract

We introduce several Ramsey-theoretic properties of 0-dimensional ambits and obtain their dynamical characterizations. In consequence, we obtain Ramsey-theoretic criteria for triviality and for profiniteness of some important invariants (in particular, of the Ellis groups) of the ambits in question. This yields a criterion for the structural property that each distal minimal factor of the given ambit is a profinite flow. Another result is a criterion for metrizability of the minimal left ideals in the Ellis semigroup. Then we study three specializations of the above abstract context: to first order theories, to definable groups, and to the classical Kechris-Pestov-Todorčević theory, recovering known and obtaining new results in each of these contexts.

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Krzysztof Krupiński, Junguk Lee, Slavko Moconja. 2026-09-20. Ramsey theory and topological dynamics of 0-dimensional flows. https://arxiv.org/abs/2609.25132

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