Analysis shows smoothness is key for strong and weak Borel Ramsey properties in countable Borel equivalence relations.
We define some natural notions of strong and weak Borel Ramsey properties for countable Borel equivalence relations and show that they hold for a countable Borel equivalence relation if and only if the equivalence relation is smooth. We also consider some variation of the notion for hyperfinite non-smooth Borel equivalence relations.
No takes yet. Share an insight, caveat, or question.
Gao et al. (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: