English

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}
}