An automorphism group of an omega-stable structure that is not locally (OB)

TL;DR

The paper presents an example of an automorphism group of an omega-stable model that is not locally (OB), addressing a question in model theory and group actions.

Contribution

It provides the first known example of such an automorphism group, specifically in the context of uncountably-categorical theories, expanding understanding of automorphism groups in model theory.

Findings

Existence of an automorphism group of an omega-stable model that is not locally (OB)

Answers a previously open question by C. Rosendal

Highlights new behaviors of automorphism groups in stable theories

Abstract

We observe that there is an example of an automorphism group of a model of an omega-stable theory---in fact, the prime model of an uncountably-categorical theory---that is not locally (OB), answering a question of C. Rosendal.