Complete orbit equivalence relation and non-universal Polish groups

TL;DR

The paper demonstrates that non-universal Polish groups can generate complete orbit equivalence relations, resolving a previously open question in the field.

Contribution

It establishes that non-universal Polish groups are capable of inducing complete orbit equivalence relations, expanding understanding of their complexity.

Findings

Non-universal Polish groups can induce complete orbit equivalence relations.

Answers a question posed by Sabok regarding orbit equivalence relations.

Expands the classification of Polish groups based on their induced relations.

Abstract

We show that a non-universal Polish group can induce a complete orbit equivalence relation, which answers a question of Sabok from \cite{OPENPROBLEMS}.