3 papers
math.LO2024
Borel Order Dimension
Dilip Raghavan, Ming Xiao
We introduce and study a notion of Borel order dimension for Borel quasi orders. It will be shown that this notion is closely related to the notion of Borel dichromatic number for…
math.LO2024
An order analysis of hyperfinite Borel equivalence relations
Su Gao, Ming Xiao
In this paper we first consider hyperfinite Borel equivalence relations with a pair of Borel -orderings. We define a notion of compatibility between such pairs, and pro…
math.LO2024
The Borel Ramsey properties for countable Borel equivalence relations
Su Gao, Ming Xiao
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 relati…