3 citations · 3 across the 6 of their papers we have counts for
6 papers
The class and dynamics of -balanced Polish groups
Shaun Allison, Aristotelis Panagiotopoulos
For each ordinal , we introduce the class of -balanced Polish groups. These classes form a hierarchy that completely stratifies the space between the class of Polish grou…
Countable Borel treeable equivalence relations are classifiable by
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…
Classification Strength of Polish Groups: Involving
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…
Actions of tame abelian product groups
Shaun Allison, Assaf Shani
A Polish group is tame if for any continuous action of , the corresponding orbit equivalence relation is Borel. When for countable abelian , Solecki (…
Non-Archimedean TSI Polish groups and their potential Borel complexity spectrum
Shaun Allison
A variation of the Scott analysis of countable structures is applied to actions of non-Archimedean TSI Polish groups acting continuously on a Polish spaces. We give results on the…
Dynamical obstructions to classification by (co)homology and other TSI-group invariants
Shaun Allison, Aristotelis Panagiotopoulos
In the spirit of Hjorth's turbulence theory, we introduce "unbalancedness": a new dynamical obstruction to classifying orbit equivalence relations by actions of Polish groups which…