Rooted trees, strong cofinality and ample generics

TL;DR

This paper characterizes certain countable rooted trees based on properties of their automorphism groups, specifically focusing on uncountable strong cofinality and ample generics.

Contribution

It provides a characterization of rooted trees whose automorphism groups exhibit uncountable strong cofinality or contain open subgroups with ample generics.

Findings

Identifies conditions for uncountable strong cofinality in automorphism groups.

Determines when automorphism groups have open subgroups with ample generics.

Abstract

We characterize those countable rooted trees whose full automorphism group has uncountable strong cofinality or contains an open subgroup with ample generics.