Shaun Allison

activity

20212024

collaborators

4 papers

math.LO2024

The class and dynamics of $α$ -balanced Polish groups

Shaun Allison, Aristotelis Panagiotopoulos

For each ordinal $α < ω_{1}$ , we introduce the class of $α$ -balanced Polish groups. These classes form a hierarchy that completely stratifies the space between the class of Polish grou…

math.LO2023

Countable Borel treeable equivalence relations are classifiable by $ℓ_{1}$

Shaun Allison

Gao and Jackson showed that any countable Borel equivalence relation (CBER) induced by a countable abelian Polish group is hyperfinite. This prompted Hjorth to ask if this is in fa…

math.LO2023

Classification Strength of Polish Groups: Involving $S_{\infty}$

Shaun Allison

In recent years, much work has been done to measure and compare the complexity of orbit equivalence relations, especially for certain classes of Polish groups. We start by introduc…

math.LO2021

Actions of tame abelian product groups

Shaun Allison, Assaf Shani

A Polish group $G$ is tame if for any continuous action of $G$ , the corresponding orbit equivalence relation is Borel. When $G = \prod_{n} Γ_{n}$ for countable abelian $Γ_{n}$ , Solecki (…

The class and dynamics of α-balanced Polish groups

Countable Borel treeable equivalence relations are classifiable by ℓ1​

Classification Strength of Polish Groups: Involving S∞​

Actions of tame abelian product groups

The class and dynamics of $α$ -balanced Polish groups

Countable Borel treeable equivalence relations are classifiable by $ℓ_{1}$

Classification Strength of Polish Groups: Involving $S_{\infty}$