The Borel Ramsey properties for countable Borel equivalence relations
Logic
2025-03-28 v2 Combinatorics
Abstract
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.
Keywords
Cite
@article{arxiv.2401.14605,
title = {The Borel Ramsey properties for countable Borel equivalence relations},
author = {Su Gao and Ming Xiao},
journal= {arXiv preprint arXiv:2401.14605},
year = {2025}
}